PHY C3: Newton’s Laws of Motion

What is Newton's 1st Law of Motion?

A body continues in its state of rest or uniform motion in a straight line, unless a resultant external force acts on it.

What does Newton's 1st Law imply for the state of rest?

Requires no resultant force to maintain.

What does Newton's 1st Law imply for uniform velocity?

Also requires no resultant force to maintain.

What concept does Newton's 1st Law give rise to?

The concept of force: a quantity that can cause a body to undergo a change in velocity (or momentum).

What is Newton's 2nd Law of Motion?

The rate of change of momentum (p) of a body is proportional to the resultant force (FR) acting on it and occurs in the direction of the force.

What is the mathematical form of Newton's 2nd Law?

FR = k (dp/dt).

What is the value of 'k' in SI units for Newton's 2nd Law?

k = 1.

What is the general formula for Newton's 2nd Law in SI units?

FR = dp/dt = d(mv)/dt.

What is the meaning of force derived from Newton's 2nd Law?

Force is a quantity that changes the motion of the body.

What does Newton's 2nd Law imply for stopping a body with larger momentum?

Requires either a larger force (in the same time) or a longer time (with the same force).

What is Newton's 2nd Law for Constant Mass (m)?

FR = m (dv/dt) = ma.

What is a Newton (N)? (Definition)

The force acting on a body of mass 1 kg which causes the body to accelerate at 1 m s⁻² in the same direction of the force.

What is the direction of acceleration?

In the same direction as the resultant force FR.

What is Newton's 2nd Law for Constant Mass Flow?

FR = Δv (dm/dt).

What is Newton's 3rd Law of Motion?

Whenever body A exerts a force on body B, body B exerts an equal in magnitude and opposite in direction force on body A.

What is the mathematical form of Newton's 3rd Law?

|FA on B| = |FB on A| and FA on B = -FB on A.

What are action-reaction pairs of forces?

The forces FA on B and FB on A are known as action-reaction pairs.

What are the conditions for two forces to be an action-reaction pair?

They must be of the same type and act on different bodies (thus they do not cancel each other out).

What is the Problem-Solving Technique for Solving Dynamical Problems?

1. Select body/system for analysis.

2. Draw free-body diagram showing all forces.

3. Select a positive direction (conveniently, direction of acceleration).

4. Determine F_net = Σ(all forces).

5. Apply Newton's 2nd Law: F_net = ma to body/system.