Overview
This lecture covers Newton's three laws of motion, their physical meanings, and problem-solving applications involving forces, acceleration, and momentum.
Newton's First Law (Law of Inertia)
- An object at rest remains at rest unless acted on by a net (unbalanced) force.
- An object in motion continues in motion with constant velocity unless acted on by a net force.
- If the net force on an object is zero, the object's velocity remains constant (including rest).
- Common examples: box on a surface (forces balanced), ball rolling on ice (little friction).
Newton's Second Law
- The net force on an object equals mass times acceleration: ( F_{net} = m \times a ).
- If acceleration is zero, net force is zero; if net force is zero, acceleration is zero.
- If mass increases and force stays constant, acceleration decreases (and vice versa).
- Acceleration is the rate of change of velocity: ( a = \Delta v / \Delta t ).
- Newton's Second Law can also be expressed as: net force equals the rate of change of momentum (( F_{net} = \Delta p / \Delta t )).
- Impulse (force × time) equals change in momentum (( F \cdot \Delta t = m \cdot \Delta v )).
Newton's Third Law
- For every action, there is an equal and opposite reaction (( F_{A} = -F_{B} )).
- Forces always occur in pairs with equal magnitude and opposite directions.
- Example: throwing a ball from a boat causes the boat to move in the opposite direction.
- Objects with smaller mass experience greater acceleration for the same force.
Problem Solving & Examples
- Constant velocity → net force is zero; acceleration is zero.
- To maintain constant velocity against friction, engine/applied force must equal friction force.
- Acceleration on a frictionless surface: ( a = F / m ).
- To find speed after time with constant acceleration: ( v_f = v_i + a t ) (if ( v_i = 0 ), ( v_f = a t )).
- Distance under constant acceleration: ( d = v_i t + \frac{1}{2} a t^2 ).
- For momentum and impulse calculations: ( p = m \cdot v ); impulse = change in momentum.
Key Terms & Definitions
- Net Force — The vector sum of all forces acting on an object.
- Inertia — The tendency of an object to resist changes in its motion.
- Momentum (( p )) — Product of mass and velocity (( p = m \cdot v )).
- Impulse — Change in momentum (( F \cdot \Delta t )).
- Acceleration (( a )) — Rate of change of velocity (( a = \Delta v / \Delta t )).
- Normal Force — The force exerted by a surface perpendicular to the object.
Action Items / Next Steps
- Review and practice applying Newton's three laws to word problems.
- Memorize key formulas: ( F = m a ), ( a = \Delta v / \Delta t ), ( d = v_i t + \frac{1}{2} a t^2 ).
- Work through textbook problems involving force, acceleration, and momentum.