Mr.p: Good morning. Let’s review as much of the AP Physics 1 curriculum as we can in 30 minutes. Billy: Absolutely! Bobby: Uh. Bo: Sure. ♪ Flipping Physics ♪ Mr.p: Okay, the basic idea here is that I am taking the more than 3 and a half hours of AP Physics 1 review videos I have in the playlist linked below and distilling it down as much as possible. Clearly I cannot review everything in such a short amount of time. Feel free to use my longer review playlist if you have the time, however, I am making this much shorter review on the idea that y’all can use it as a refresher right before the exam. And, because I want to move as quickly as possible to review as much as possible, I am not going to be asking or answering any questions. Are y’all going to be okay with that? Bobby: Absolutely. Bo: Sure. Billy: … Okay. Mr.p: And, before we get started I do need to mention that, if you are looking for practice exams which mirror the digital exam, you can purchase my AP Physics 1 Ultimate Exam Slayer, which also includes resources to help you understand the structure of exam, and if you are looking to gain a better understanding of the curriculum you can purchase my AP Physics 1 Ultimate Review packet, which also includes a practice exam. Links for both of those are below, in the video description. Alright, are we ready? Billy: Hot to trot! Bobby: All systems go! Bo: Sure. Mr.p: (Good. Here we go. Unit 1: Kinematics. Vectors have magnitude and direction. Scalars have magnitude only.) The distance an object travels is the length of the path taken between initial and final position. The displacement of an object is the straight-line distance between the object’s initial and final points or change in position equals final position minus initial position. Displacement is a vector and distance is a scalar. That means the distance an object travels will always be greater than or equal to the magnitude of the displacement of the object. Average velocity equals displacement over change in time, and velocity is a vector. Average acceleration equals change in velocity over change in time, and acceleration is a vector. If the time interval over which the velocity or acceleration is taken is very small, then the velocity or acceleration is considered to be instantaneous, in other words what it would be at a specific time, rather than over a time period. If the acceleration of an object is constant, then we can use the uniformly accelerated motion equations or UAM equations – they are also called kinematics equations – to analyze the motion of the object. In the uniformly accelerated motion equations there are 5 variables, 4 equations, and if you know three of the variables, you can find the other 2, which leaves you with … All: (1 happy physics student.) Mr.p: The slope of a position vs. time graph is velocity. The slope of a velocity vs. time graph is acceleration. The area between the curve and the time axis on a velocity vs. time graph is change in position. The area between the curve and the horizontal time axis on an acceleration vs. time graph is change in velocity. And area above the horizontal axis is positive and area below the horizontal axis is negative. We will often have to break, or resolve, vectors into their component vectors using the sine and cosine trigonometric functions. Be careful to remember theta will not always be measured from the horizontal, therefore, the x-component will not always use cosine. If the only force acting on an object is the gravitational force and the object is near the surface of the Earth, the object is in projectile motion and the acceleration of the object in the y-direction equals 9.81 meters per second squared down, however, on the AP Physics exams you should use 10 meters per second squared instead. Realize the acceleration of the object in the y-direction is constant, so you can use the UAM equations in the y-direction. In the x-direction the acceleration of the object is zero and you can use the equation for constant velocity in the x-direction. The description of the motion of an object changes depending on the frame of reference of the person observing the motion. This is called relative motion and often involves vector addition. Unit 2: Force and Translational Dynamics. The center of mass of a system of particles equals the sum of the expression mass of each particle times the position of each particle relative to a zero-reference line all divided by the total mass of the particles. This equation is also valid if you replace each position variable with a velocity variable or an acceleration variable. All forces are vectors and are the result of an interaction between two objects. Always. Free Body Diagrams show all the forces acting on an object. Only force vectors should be in free body diagrams. All forces start at the center of mass of the object or system. If there are two or more forces acting in the same direction on an object, those forces still start at the center of mass of the object, they are simply offset from one another. Never break forces into components in a free body diagram answer on an AP Physics exam. The force normal caused by a surface is always perpendicular to the surface and pushes away from that surface. The force of tension in a rope or something similar is always parallel to the direction of the rope and a pull. Newton’s First Law states that, “An object at rest will remain at rest and an object in motion will remain at a constant velocity unless acted upon by a net, external force.” This is often called the Law of Inertia because inertia is the tendency of an object to resist acceleration. Newton’s Second Law is an equation which relates net force, mass, and acceleration. On the AP Physics 1 reference sheet it is shown as the acceleration of the system equals the net force acting on the system divided by the mass of the system where both acceleration and force are vectors. When the net force on an object is zero, the object is in translational equilibrium. That means the object is either at rest or moving at a constant velocity because the acceleration of the object equals zero. Newton's Third Law states that for every force object one exerts on object two, object two exerts a force on object one that is equal in magnitude and opposite in direction, and these forces act simultaneously. The magnitude of the gravitational force exerted on a mass in a gravitational field is determined using the equation force of gravity equals mass times gravitational field strength. The direction of the force of gravity on an object is always towards the center of mass of the planet; down. The direction of the force of friction is always parallel to the surface, always opposes sliding motion, and always independent of the direction of the force applied. The force of kinetic friction equals the coefficient of kinetic friction times force normal. Kinetic friction occurs when the two surfaces are sliding relative to one another. The coefficient of friction, mu, has no units, cannot be negative, and is experimentally determined. The force of static friction is less than or equal to the coefficient of static friction times force normal. Static friction only occurs when the two surfaces are not sliding relative to one another. The force of static friction adjusts in an attempt to keep the two surfaces from sliding relative to one another. The force of friction does not depend on the size of the surface area of contact between the two surfaces. The magnitude of the gravitational force using Newton’s Law of Universal Gravitation equals the gravitational constant … Billy: (Big G!) Mr.p: times mass 1 times mass 2 divided by the square of the distance between centers of mass. The gravitational force is always directed along a line connecting the centers of mass of the two objects and is always directed toward the other mass. The local gravitational field on a planet, little g, is nearly constant on the surface of the planet. The magnitude of the gravitational field can be found by setting the two equations for gravitational force equal to one another. An ideal spring force is proportional to its displacement from equilibrium position and the equation for the spring force is called Hooke’s Law, where the force of the spring equals the negative of the quantity spring constant times the displacement from equilibrium position of the spring. The direction of the spring force is always toward equilibrium position. The negative in Hooke's law represents that the spring force and the displacement of the object from equilibrium position are opposite in direction. The magnitude of the slope of a graph of spring force vs. displacement from equilibrium position is the spring constant, because y equals m x plus b. The linear velocity of an object moving along a circular path is called tangential velocity which is always directed perpendicularly to the radius describing the path and parallel to the path itself. An object moving along a circular path, must have a centripetal acceleration which is always directed inward toward the center of the circle. The reason an object moving along a circular path must have a centripetal acceleration is because the direction of the tangential velocity of the object is always changing. Centripetal acceleration equals the square of tangential speed divided by radius. The time it takes an object which is moving along a circular path at a constant speed to complete one circle is defined as period, capital T. The number of revolutions completed by the object per second is defined as frequency, lowercase f. And period equals the inverse of frequency. Centripetal force is the net force in the in-direction which causes the centripetal acceleration of the object in toward the center of the circle. The net force in the in-direction, the centripetal force, equals mass times centripetal acceleration, is not a new force, and is never in a free body diagram. The in direction is positive, and the out direction is negative. Unit 3: Work, Energy, and Power. An object whose center of mass is moving has translational kinetic energy, one-half mass times speed squared. Work is the amount of mechanical energy transferred into or out of a system and it equals the magnitude of the force doing the work on the system times the magnitude of the displacement of the system while the force acts, times the cosine of the angle between the direction of the force and the displacement. The work done by a conservative force on a system is independent of the path of the object. Two examples of conservative forces are the gravitational force and the spring force. The work done by a nonconservative force on a system does depend on the path of the object. Two examples of nonconservative forces are the force of friction and the force of air resistance. The three types of mechanical energy are kinetic energy, gravitational potential energy, and elastic potential energy. Potential Energy is the energy stored in a system due to the positions of the objects in the system. In a constant gravitational field, the change in gravitational potential energy equals mass times gravitational field strength times the change in vertical position of the object. A single object cannot have potential energy. The general form for the gravitational potential energy which exists between two objects with mass equals the negative of the gravitational constant … Billy: (Big G!) Bobby: (Dude. Let him do his thing!) Mr.p: times mass 1 times mass 2 all divided by the distance between the centers of mass of the two objects. The location of zero gravitational potential energy in this equation is where the two objects are infinitely far away from one another. This is why the general form of gravitational potential energy is always negative. Elastic potential energy equals one-half times the spring constant times displacement from equilibrium position squared. Work and Energy are scalars. This means Work, Kinetic Energy, Gravitational Potential Energy, and Elastic Potential Energy do not have direction, they only have magnitude. A system with only one object in it can only have kinetic energy. Any changes to the types of energies in a system are balanced by equivalent changes of other types of energies in the system or by a transfer of energy into or out of the system. The total mechanical energy of a system remains the same if there is zero net work done on the system and there is zero work done by nonconservative forces. When there is net work done on a system, energy is transferred between the system and its surroundings. When friction does work on the system and no external forces add or remove energy from the system, the work done by the nonconservative force equals the change in mechanical energy of the system. The work-energy principle states that the net work done on a system equals the change in kinetic energy of the system. This equation is always valid, even if friction does work on the system and an external force adds or removes energy from the system. Whenever you are using these equations where mechanical energy remains constant or energy is transferred into or out of a system, in addition to clearly identifying the system, you always have to identify the initial point, the final point, and the horizontal zero line. Power is the rate at which energy changes with respect to time, by either being transferred into or out of a system or converted from one type of energy to another within a system. Average power delivered to a system equals the work done on the system divided by the change in time during which that work was done. Instantaneous power equals the magnitude of the force doing the work on the object, times the magnitude of the velocity of the object, times the cosine of the angle between the directions of the force and the velocity. Unit 4: Linear Momentum. Linear momentum, which is a vector, equals mass times velocity. In AP Physics 1 during all collisions and explosions, the net external force acting on the object or system is considered to be negligibly small relative to the forces internal to the system, and during an explosion, forces internal to the system push the objects in the system apart. Newton’s Second Law in terms of momentum is net force equals change in momentum over change in time. Impulse, uppercase J, which is a vector, equals change in momentum, it equals average force times change in time, and it equals the area “under” a force versus time curve. When the net force acting on a system is zero, the impulse on ths system is also zero, so the momentum of the system remains constant because no momentum is added or removed from the system. In other words, the sum of the initial momenta equals the sum of the final momenta. If the net force acting on a system with several objects in it is zero, the velocity of the center of mass of the system is constant. This is because the change in momentum of the system is zero. When the net force on a system is nonzero, linear momentum does not remain constant because linear momentum is transferred between the system and the environment. There are three main types of collisions. They are: elastic collisions where the total kinetic energy of the system before the collision is the same as the total kinetic energy after the collision. Inelastic collisions where the total kinetic energy of the system decreases during the collision. And perfectly inelastic collisions which are inelastic collisions where the objects stick to one another after the collision. Most real-world collisions are inelastic collisions. During all collisions, because the net external force acting on the system is considered to be negligibly small relative to the internal forces, the linear momentum of the system remains constant. Unit 5: Torque and Rotational Dynamics. Angular displacement equals angular position final minus angular position initial. The units for angular displacement are degrees, radians, and revolutions, however, to use angular displacement, and all other angular variables in pretty much any physics equation, it needs to be in radians. One revolution equals 360 degrees which equals 2 pi radians. Average angular velocity equals angular displacement over change in time. Average angular acceleration equals change in angular velocity over change in time. Rigid objects with shape maintain a constant shape as they rotate, this means all points in a rigid object go through the same angular displacement during the same time interval, have the same angular velocity, and have the same angular acceleration. If the angular acceleration of the object is constant, the object is experiencing uniformly angularly accelerated motion. Billy: (U fishy M!) Bobby: (Dude.) Bo: (You need to stop.) Billy: (Okay. I just get so excited.) Bo: (I know. I know.) Mr.p: And there are four U fishy M equations which are just like the UAM equations only with rotational variables rather than linear variables. In graphs of rotational motion, the slope of an angular position as a function of time graph is angular velocity. The slope of an angular velocity as a function of time graph is angular acceleration. The area “under” an angular acceleration as a function of time graph is change in angular velocity. The area “under” an angular velocity as a function of time graph is change in angular position or angular displacement. An object moving along a circular path moves through an angular displacement, however, it also moves through a linear distance called arc length which equals radius times angular displacement. It also has a linear velocity called tangential velocity which equals radius times angular velocity. It can also have a linear acceleration called tangential acceleration which equals radius times angular acceleration. The directions of tangential velocity and tangential acceleration are tangent to the circular path being traced out by the object and perpendicular to the radius. In order to use each of the three equations relating a linear variable to a rotational variable, the rotational variable needs to be in radians. This is because radians are a dimensionless quantity. Centripetal acceleration equals tangential speed squared over radius. It also equals radius times angular speed squared. The three different accelerations an object can have in circular motion are angular acceleration, tangential acceleration, and centripetal acceleration. Angular acceleration is the only one of the three which is an angular quantity with units of radians per second squared. Both tangential acceleration and centripetal acceleration are linear accelerations with units of meters per second squared. Tangential acceleration is always in a direction tangent to the circular path being traced out by the object and perpendicular to the radius. Centripetal acceleration is always in a direction perpendicular to the circular path being traced out by the object and in toward the center of the circle along the radius. This means tangential acceleration and centripetal acceleration are always perpendicular to one another. Circular motion cannot exist without centripetal acceleration. Tangential acceleration refers to a change in the magnitude of the tangential velocity of an object. Centripetal acceleration refers to a change in the direction of the tangential velocity of an object. When a rigid object is rotating, the terms angular displacement, angular velocity, and angular acceleration refer to the whole object, however, the terms arc length, tangential velocity, tangential acceleration, and centripetal acceleration refer to a specific location on the object. Torque, lowercase tau, is the ability of a force to cause an angular acceleration of an object and it equals r, the distance from the axis of rotation to the location where the force acts on the object, times F, the force causing the torque, times the sine of theta, the angle between the directions of r and F. r sub perpendicular is called the lever arm which is the perpendicular distance from the axis of rotation to the line of action of the force. Torque is a vector, however, this equation for torque is the magnitude of the torque. In AP Physics 1 we use clockwise and counterclockwise to indicate the direction of torque. When working with torque we draw force diagrams of all the forces acting on an object. The objects are no longer point particles; they are rigid objects with shape. This means we need to indicate in our force diagram where the forces act on the object. Rotational inertia, uppercase I, is a measure of how much an object resists angular acceleration. The equation for rotational inertia of a point particle rotating around an axis of rotation is the mass of the point particle times the square of r, the distance between the axis of rotation and the location of the point particle. To get the rotational inertia of a system of particles, we add up the rotational inertias of each particle in the system. When needed, the equations for rotational inertias of rigid objects with shape will be provided on the AP Physics 1 exam. In order to determine the rotational inertia of a particle, a system of particles, or a rigid object with shape, you must first identify the axis of rotation. If you have the equation for the rotational inertia of a uniform, rigid object with shape about an axis through its center of mass, you can determine the rotational inertia of that object about another axis which is parallel to the axis through the center of mass by using the Parallel Axis Theorem which states that the new rotational inertia equals the rotational inertia of the object about an axis through its center of mass plus the mass of the object times the square of the distance between the two axes. When a system is in rotational equilibrium, the angular velocity of the system is constant. Newton’s First Law in Rotational Form is: An object at rest remains at rest, and a rotating object maintains a constant angular velocity, unless acted upon by a net, external torque or the distribution of the mass of the object changes. Newton’s Second Law in rotational form is net torque equals rotational inertia times angular acceleration. From this we can see that the rotational equivalent of force is torque, the rotational equivalent of mass is rotational inertia, and the rotational equivalent of linear acceleration is angular acceleration. An object which is at rest and is not rotating is in both translational and rotational equilibrium, this is called static equilibrium. In static equilibrium the net torque about any axis of rotation is equal to zero. This means you can pick an axis of rotation which makes the math easier. Unit 6: Energy and Momentum of Rotating Systems. Objects whose center of mass is changing location have Translational Kinetic Energy and objects that are rotating have Rotational Kinetic Energy which equals one-half rotational inertia times angular speed squared. The total kinetic energy of a rigid object is the addition of its rotational kinetic energy about its center of mass and its translational kinetic energy from the linear motion of its center of mass. A torque can transfer energy into or out of a rigid system if the torque acts over a change in angular position or angular displacement. Work done by a constant torque on a rigid system equals torque times angular displacement. On a graph of torque as a function of angular position, work is the area “under” the curve. Angular Momentum of a Rigid Object with Shape equals rotational inertia times angular velocity. Angular momentum is a vector. Angular momentum of a rigid object with shape has to be relative to an axis of rotation. Angular Momentum of a Point Particle equals r, the distance from the axis of rotation, or reference line, to the point particle, times the mass of the point particle, times the magnitude of the velocity of the point particle, times the sine of the angle between r and v. Angular momentum of a point particle has to be relative to an axis of rotation, which is sometimes called a reference line. And, while this equation is for the magnitude of the angular momentum of a point particle, angular momentum is a vector. Again, in AP Physics 1 we use clockwise and counterclockwise to indicate the direction of angular momentum. Another rotational form of Newton’s Second Law is net torque equals change in angular momentum over change in time, and when you move change in time over to the other side of the equation, you can see angular impulse equals change in angular momentum which equals torque times change in time and that equals the area “under” a torque versus time curve. On a graph of angular momentum as a function of time, the slope of the curve is the net torque acting on the object. The total angular momentum of a system remains constant if the net torque acting on the system equals zero. When that occurs, no angular momentum is added or removed from the system. A rigid object with shape which is rolling without slipping has equations for the displacement, velocity, and acceleration of its center of mass which are very similar to the circular motion equations for arc length, tangential velocity and tangential acceleration. For example, in circular motion the tangential velocity of a location on an object equals the distance from the axis of rotation to the location on the object times the angular velocity of the object, and in rolling without slipping the velocity of the center of mass of the object equals the radius of the object times the angular velocity of the object. When an object is rolling without slipping it has both translational and rotational kinetic energies. The acceleration of a rigid object with shape rolling without slipping on an incline only depends on three variables: the incline angle, the gravitational field, and the factor in front of mass times radius squared in the rotational inertia equation. When an object is rolling WITH slipping, the equations for rolling without slipping are no longer valid. For example, the velocity of the center of mass of an object rolling with slipping does not equal the radius of the object times its angular velocity. In circular orbits, the total mechanical energy of the system, the gravitational potential energy of the system, angular momentum of the satellite, and the kinetic energy of the satellite all remain constant. In elliptical orbits the total mechanical energy of the system and the angular momentum of the satellite remain constant, however, the gravitational potential energy of the system and the kinetic energy of the satellite do not remain constant. When a satellite is in a circular orbit or an elliptical orbit around a planet its linear momentum does not remain constant because the direction of its velocity changes, however, the angular momentum of the satellite does not change; the direction of its angular velocity does remain constant. Escape velocity is defined as the initial speed necessary directed away from the surface of a planet such that the final velocity of the object will be zero when the object is an infinite distance from the planet. Unit 7: Oscillations. Periodic motion is motion which is repeated in equal intervals of time. Simple Harmonic Motion is periodic motion which results from a restoring force acting on an object where the magnitude of that force is proportional to the displacement of the object from equilibrium position. Equilibrium position is the location where the net force acting on the object is zero. A restoring force is always directed towards equilibrium position. The period of simple harmonic motion, capital T, is defined as the time it takes to go through one full cycle or oscillation. The amplitude of simple harmonic motion, capital A, is defined as the maximum distance from equilibrium position. Just one example of a system going through one full simple harmonic motion cycle would be this horizontal, ideal mass-spring system going through the following positions, 2, 3, 2, 1, 2. At position 1 the displacement of the mass from equilibrium is at its maximum value, the amplitude, the velocity of the mass is zero, the spring force and acceleration of the mass are at their maximum magnitudes, and the spring force and acceleration are directed to the left. At position 2 the displacement of the mass from equilibrium is zero, the velocity of the mass is at its maximum magnitude, the spring force and acceleration are both zero, and the velocity of the mass is either to the left or right. At position 3 the displacement of the mass from equilibrium is at its maximum magnitude in the negative direction, the negative of the amplitude, the velocity of the mass is again zero, the spring force and acceleration of the mass are again at their maximum magnitudes, and the spring force and acceleration are directed to the right. The period of a mass-spring system equals 2 pi times the square root of mass divided by spring constant. The restoring force for a horizontal mass-spring system is the spring force acting on the mass. The period of a simple pendulum equals 2 pi times the square root of the length of the pendulum divided by gravitational field strength. A simple pendulum is considered to be in simple harmonic motion for small angles. For AP Physics 1 the maximum angle can be as large at 15°. The restoring force for a simple pendulum is the component of the force of gravity acting on the pendulum bob which is tangent to the direction of the motion of the bob. Frequency of simple harmonic motion is defined as the number of cycles, or oscillations, per second. An equation which can describe the position of an object in simple harmonic motion is position equals amplitude times the cosine of the quantity 2 pi times frequency times time. The only difference between using cosine and sine in this equation is that they are phase shifted from one another by a magnitude of 90 degrees or pi over 2 radians. In other words, when you use cosine the initial position of the object is the amplitude, and when you use sine, the initial position of the object is the equilibrium position. These are the graphs of position, velocity, and acceleration of a mass-spring system moving through positions 1, 2, 3, 2, and 1. You can see these graphs match everything I stated previously about position, velocity, and acceleration at locations 1, 2, and 3; however, these also help you visualize what those values are between locations 1, 2, and 3. The total mechanical energy of an object in simple harmonic motion is the sum of the kinetic energy and the potential energy of the system. The total mechanical energy of an isolated system in simple harmonic motion is constant. The total mechanical energy of a horizontal, ideal mass-spring system equals one-half spring constant times amplitude squared. It also equals one-half mass times maximum speed squared. Set these two equations equal to one another and you can solve for the maximum speed of a horizontal, ideal mass-spring system. Unit 8: Fluids. Density, or rho, equals mass divided by volume. Pressure on a surface equals the force perpendicular to the surface divided by the surface area. Pressure is a scalar. The absolute pressure at any point in a fluid is the sum of the pressure on the top of the fluid and the gauge pressure caused by the weight of the vertical column of fluid above that point. Gauge pressure equals fluid density times gravitational field strength times fluid depth and gauge pressure does not depend on the cross-sectional area of the container holding the fluid. The buoyant force is equal in magnitude to the weight of the fluid displaced by the object; therefore, the buoyant force equals the mass of the fluid displaced by the object times gravitational field strength or the density of the fluid displaced by the object times the volume of the fluid displaced by the object times gravitational field strength. The continuity equation for ideal fluid flow says that the volumetric flow rate, or cross-sectional area times fluid flow speed, is constant. This is true for ideal fluid flow through a closed volume like a pipe. Bernoulli’s equation is a description of mechanical energy remaining constant in ideal fluid flow. Bernoulli’s equation is pressure at point 1 plus one-half fluid density times fluid speed at point 1 squared plus fluid density times gravitational field strength times vertical height at point 1 relative to a horizontal zero line equals all of that at point 2. Bernoulli’s Principle relates fluid speed and fluid pressure. For example, assuming the difference in height is negligible, according to Bernoulli’s Principle, if fluid speed increases, fluid pressure decreases. Torricelli’s Theorem gives the speed of an ideal fluid exiting a large, open reservoir through a small hole. That speed equals the square root of 2 times gravitational field strength times the vertical height of the top of the fluid in an open reservoir above the small hole. Bobby: Well … Bo: I guess that’s it. Mr.p: Yeah, I guess that’s it. If you are looking for more help, as I said earlier, I have the Ultimate Exam Slayer with digital practice exams and more about the exam structure, I have the Ultimate Review Packet with more about the curriculum and one practice exam, I have more than 3 and a half hours of more detailed AP Physics 1 review videos, and I have almost 40 hours of AP Physics 1 topic videos. Yeah, I’ve got plenty of help for you. Links are below. Best of luck to every single one of you taking the AP Physics 1 exam. You can do this. I have confidence in you. Thank you very much for learning with me today, I enjoy learning with you.