Good morning! This is my review of roughly the
first half of Unit 2, Forces and Translational Dynamics, for AP Physics 1. This is about
Newton’s Laws, forces, and center of mass. ♪ Flipping Physics ♪
This video is a free portion of my AP Physics 1 Ultimate Review Packet. If you are planning to
take the AP Physics 1 exam, I definitely recommend you invest in my full AP Physics 1 Ultimate Review
Packet. Link is in the video description. Now, Bobby, what is the equation on the equation sheet
for the center of mass of a system of particles? Uh, x center of mass equals the sum of the mass
of particle i times the x position of particle i, all divided by the sum of the mass of particle i.
That’s confusing. Which is why mr.p usually writes it as the
x center of mass of a system of particles equals the quantity, the mass of particle
1 times the x-position of particle 1 plus the mass of particle 2 times the x-position of
particle 2 plus the ellipsis and the ellipsis represents that the equation can go on for
as many particles as are in the system, all divided by the mass of particle 1 plus the mass
of particle 2 plus and then the ellipsis again. Right. That makes more sense.
And the x position variable could be a y or a z as well. It just depends on
which direction the center of mass is defined. And we should probably mention that the position,
x, is relative to a zero point which could be the origin, however, it could be defined in some other
way, like we could end up defining it when we’re doing the problem. It just depends on the problem.
Well done everybody. And remember that this equation form can also be used to determine the
velocity or acceleration of a system of particles. We just need to replace the x-position variable
with the velocity variable or the acceleration variable. Alright, so that’s all for the center
of mass of a system of particles. Now let’s talk about the center of mass of an object with shape.
Realize an object is a collection of particles which have little to no interaction with one
another. And, often in physics, an object is treated as having no internal structure. Now,
because finding the center of mass of an object with shape requires calculus, center of mass
problems which involve objects with shape in AP Physics 1 should only include constant density
objects with obvious centers of mass or centers of mass we can estimate. For example, the center
of mass of a nearly constant density sphere is right in its center. You can see that when I toss
the sphere up and it rotates around its center of mass. The center of mass of a nearly constant
density rectangular block is right in its center, again you can see it rotates around its center
of mass and you can see the center of mass of the rectangular block is in projectile motion.
The center of mass of a nearly constant density roll of tape is right in its center, again you
can see it rotates around its center of mass in projectile motion. And we can estimate that the
center of mass of a banana is roughly here. Again, because the banana rotates around that point
when the banana is in projectile motion and the centers of mass of objects follow
the parabolic arc of projectile motion. Also, be aware that I go through several
examples of Center of Mass problems in my AP Physics 1 Review Supplement video about
Center of Mass. I definitely recommend it. Absolutely! Agreed. Yep.
Thanks. Next up, we are talking about forces. All forces are
vectors, class that means they have both …? Magnitude and direction.
Yes. And all forces are the result of an interaction between two objects. Always. Every
force involves two objects interacting with each other. Realize, this means, an object cannot exert
a force on itself. Class, when we work with forces we almost always draw a …?
Free-Body Diagram! Exactly. Free-body diagrams show all the forces
acting on an object. The only vectors which should be in free-body diagrams are force vectors.
Some examples of vectors which should never be in free-body diagrams that you may feel tempted
to add to free-body diagrams are displacement, velocity, acceleration, momentum, impulse, angular
momentum, and torque. I’m sure there are others, however, that’s all I can think of right now.
Class, all force arrows drawn in free-body diagrams start at the object’s …?
Center of mass! Which is why center of mass needed to be in
Unit 2: Forces and Translational Dynamics. Oh! That makes sense now. Right.
If there are two more forces acting in the same direction on an object, those
forces still start at the center of mass of the object or system, but you need to draw
them offset from one another. For example, in this free-body diagram of all the forces
acting on a block on a horizontal surface, the force of friction and force applied
acting on the block are both to the left, both start at the center of mass of the block
and are drawn offset from one another. And if you are having a difficult time fitting all
your forces on the dot, draw a bigger dot! How could that happen?
What? How could the force of friction and force applied
on the block be in the same direction like that? Uh
If the block is sliding to the right and a hand stops the block, as the hand is accelerating the
block to the left, the force applied by the hand is to the left and the force of kinetic friction
acts opposite the direction the block is sliding, which is also to the left. It could be that.
Oooooh. Very nice Billy. Class, do you ever break forces
into components in a free-body diagram answer on an AP Physics exam?
No! And if you need to break forces into
components, you should redraw that free-body diagram somewhere else on the exam,
not where they’ve asked you to draw your answer. Exactly.
Yup. Correct. Class, the five steps to help solve
any free-body diagram problem are. Step one? Draw the free-body diagram.
Step two? Break forces into components.
Step three? Redraw the free-body diagram.
Step four? Sum the forces.
And step five? Sum the forces.
In a direction which is perpendicular to the direction in step 4.
Yeah. Perfect. Thank you. Bobby,
tell me about the force normal. Uh, the force normal is a force caused by
a surface and the direction of the force normal is always normal to the surface or
perpendicular to the surface and the force normal always pushes away from the surface.
Nice. Bo, tell me about the force of tension. Sure. The force of tension is in a rope, string,
cable, chain, or something like that. If we have an ideal rope, then the rope does not stretch and
it has negligible mass. The force of tension in an ideal rope has the same magnitude at all points
in the rope. If the rope does not have negligible mass, then the force of tension may not be the
same at all points in the rope. For example, the force of tension in a vertically hanging
rope is the least at the bottom and the most at the top because the top of the rope has to
hold up all of the rope and the bottom of the rope barely has to hold up any rope at all.
You can actually see that in the cellular shades which cover this window. The bottom
of the shade has a small tension force in it which causes the width of each cell near
the bottom of the shade to be small, however, the top of the shade has a larger tension
force in it which causes the width of each cell near the top of the shade to be large.
Right. And the force of tension is always parallel to the direction of the rope,
wire, string, cable, or cellular shade. Thanks. These forces are examples of contact
forces. Contact forces are the result of the interaction of one object touching another object
and result from electric forces between the atoms of objects. Five examples of contact forces are
force of tension, force of friction, force normal, force applied, and the spring force. Next,
Billy, what is Newton’s First Law of Motion? Newton’s First Law of Motion 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.” And the two things students most often forget are
that an object in motion will remain at a constant velocity not just in motion and that it is “unless
acted upon by a net, external force” not just a force or an external force, but a net, external
force. Also, Newton’s First Law of Motion is often called the Law of Inertia because inertia is the
tendency of an object to resist a change in state of motion or to resist acceleration. And that
is what Newton’s First Law of Motion is about. Correct Billy. It’s also important to realize
Newton’s First Law of Motion is only valid when measurements are taken from an inertial reference
frame and that the acceleration of an inertial reference frame is zero. For example, right here
I am in a car which is driving in a circle. That means this car, this reference frame, has a
centripetal acceleration which is directed in towards the center of the circle which is
to your right. This reference frame is not an inertial reference frame. You can see that
because this block accelerates to your left when I let go of it. In this reference frame this
block accelerates without a net, external force. Again, this is not an inertial reference frame,
therefore, Newton’s First Law does not hold true in this reference frame. This block, which is at
rest, changes its state of motion with zero net, external force acting on it. Please be
aware that, on the AP Physics 1 exam, all frames of reference are assumed to be
inertial, unless otherwise stated. Next up, Bobby, what is Newton’s Second Law?
Uh, Newton’s Second Law is an equation which relates the net force acting on the center
of mass of an object or system, the mass of the object or system, and the acceleration of the
center of mass of an object or system. On the AP physics equation sheet, it is the acceleration
of the system equals the net force acting on the system divided by the mass of the system and
both acceleration and force are vectors. However, we usually use it rearranged such that
net force equals mass times acceleration. (That’s a good start, however, there’s a
lot more I need you to remember with respect to Newton’s Second Law. Who can tell me more?)
The units we typically use for forces are newtons. And a newton is a kilogram meter per second
squared. You can see that from Newton’s Second Law because force is in newtons, mass is in kilograms,
and acceleration is in meters per second squared. When using Newton’s Second Law we always
have to identify the object or system on which we are summing the forces and the
direction in which we are summing the forces. Because force and acceleration are vectors, the
acceleration of an object is always in the same direction as the net force on the object.
Great. Thanks. We should also talk about translational equilibrium. Class, what can
you tell me about translational equilibrium? When an object is in translational equilibrium
the net force on the object equals zero. Translational equilibrium means
the object is either at rest or moving at a constant velocity because the
acceleration of the object equals zero. If an object is at rest, there could be forces
acting on the object from other objects, however, the net force acting on the object is zero.
Perfect. And now Newton’s Third Law. Bo? Newton's Third Law is an equation: for every
force object one exerts on object two, object two exerts an equal but opposite force on object one.
Those two forces act simultaneously. And, forces internal to a system do not change the motion
of the center of mass of the system. That’s it. Yep. Next up is the gravitational force. The
interaction between an object with mass and another object with mass is described by the
gravitational force. And please realize the terms “gravitational force”, “force of gravity”,
and “weight” all mean the same thing. Also, to be clear, because all forces are
interactions between two objects, the gravitational force is always between two
objects. 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 the gravitational
field strength. And the gravitational force exerted on a mass in a gravitational field is in
the same direction as the gravitational field. We will define the term “gravitational field”
in our next AP Physics 1 review video. For now, we are just going to recognize that the magnitude
of free fall acceleration and the gravitational field are the same and both are identified using
the letter little g. The direction of the force of gravity on an object is always toward the center
of mass of the planet or down. And the two objects which are interacting in this gravitational
force equation are the object and the planet causing the gravitational field. And now that we
have discussed both Newton’s Second Law and the gravitational force equation, we can specifically
identify inertial mass and gravitational mass. Inertial mass is the measure of an object’s
inertia or a measure of an object’s resistance to acceleration. Inertial mass is the mass in
Newton’s Second law. Gravitational mass is the mass used to determine the force of gravity, or
weight, of an object. Gravitational mass is the mass in the gravitational force equation. Inertial
mass and gravitational mass are mathematically equivalent and that has been experimentally
verified. That means, in this class, unless otherwise indicated, we will simply refer to both
inertial mass and gravitational mass as “mass” and not concern ourselves with the difference between
the two. And now, the force of friction. Bobby, tell me the three things I asked you to remember
about the direction of the force of friction. The direction of the force of friction
is always parallel to the surface, always opposes sliding motion, and is independent
of the direction of the force applied. Thank you Bobby. The equation for the force of
friction as given on the equation sheet is the magnitude of the force of friction is less
than or equal to the coefficient of friction times the magnitude of the force normal. In
other words, the coefficient of friction, mu, is a ratio of the maximum force
of friction and the force normal. Bo, tell me more about the coefficient of friction.
The coefficient of friction has no units, cannot be negative, is typically in the range of
somewhere between 0 and 2, and is experimentally determined. I mean, it just depends on how rough
or smooth the two interacting surfaces are. Thanks Bo. When the two surfaces
are sliding relative to one another, the friction is kinetic and the equation
works out to be the force of kinetic friction equals the coefficient of kinetic
friction times the force normal. Billy, tell me what happens when the two surfaces
are not sliding relative to one another. Absolutely! When the two surfaces are not sliding
relative to one another the friction is static friction. The equation then is the force of static
friction is less than or equal to the coefficient of static friction times the force normal. What
happens then is that the force of static friction adjusts in an attempt to keep the two surfaces
from sliding relative to one another. That’s what the less than or equal to sign means in the
equation. The maximum force of static friction which would prevent an object from sliding
on a surface is the force of static friction maximum equals the coefficient of static friction
times the force normal. Also, for two surfaces, the coefficient of static friction is almost
always more than the coefficient of kinetic friction. In other words, it takes more force to
put an object into motion that it takes to keep an object moving. And the force of friction
does not depend on the size of the surface area of contact between the two surfaces.
Well done Billy, thanks. Now that we have discussed all of these forces, let’s discuss
a simple free-body diagram. Here I am pushing horizontally on a book on a vertical wall. Bobby,
please identify all the forces in the free-body diagram of the book, their directions, and your
reasoning for all of those forces and directions. Sure. You are pushing horizontally to the left on
the book, so that is the direction of the force applied on the book. The force of gravity on the
book acts straight down toward the center of the planet. The surface is causing a force normal
on the book which is normal, or perpendicular, to the surface and a push. So, the force normal
is to the right. ... The book is not sliding down the surface, so there must be a force of
friction parallel to the surface and opposing the sliding motion of the book, so the force of
static friction, because the two surfaces are not moving relative to one another, is upward.
I thought the force of friction was independent of the direction of the force applied.
Why are the two perpendicular to one another in this free-body diagram?
That’s just how it worked out for this free-body diagram. In the free-body
diagram mr.p did before of the sliding block, the force applied and force of kinetic
friction were in the same direction. Oh, right. Are this force applied and force
normal a Newton’s Third Law force pair? Uh, no. Those two forces act on the same object,
so they cannot be a Newton’s Third Law force pair. The force applied acts to the left from mr.p’s
hand on the book. There is an equal but opposite force applied which acts to the right from
the book on mr.p’s hand. Those two forces are a Newton’s Third Law force pair.
And the force normal acts to the right from the wall on the book. There is an
equal but opposite force normal which acts to the left from the book on the wall.
Those are a Newton’s Third Law force pair. Oh, I get it. The force of static friction acts
upward from the wall on the book. That means there is an equal but opposite force of static
friction which acts downward from the book on the wall. Those are a Newton’s Third Law force
pair. And the force of gravity acts downward from the Earth on the book. That means there is
an equal but opposite force of gravity which acts upward from the book on the Earth. Those are
also a Newton’s Third Law force pair. Nice. Well done. I do want to take a moment to talk
about how we typically address forces when an object is on an incline. Usually, we break the
force of gravity into its components which are parallel and perpendicular to the incline. The
force of gravity perpendicular equals mass times gravitational field strength times the cosine of
the incline angle. The force of gravity parallel equals mass times gravitational field strength
times the sine of the incline angle. And, please remember that the force of gravity parallel
to an incline is always directed down the incline, always. Also, if you’ve made it this far and have
not liked this video, subscribed to my channel, and rung the bell for my channel, what
exactly are you waiting for, an invitation? Thank you very much for learning with
me today, I enjoy learning with you.