A.2 Forces and Momentum

Forces are interactions that change the motion of bodies. This section explores how forces relate to acceleration and momentum, the conservation laws governing collisions, and the mechanics of circular paths.

Core Laws & Concepts

Newton’s 1st Law: A body remains at rest or constant velocity unless acted upon by a net force.
Newton’s 2nd Law: The resultant force is proportional to the rate of change of momentum (or $F=ma$ for constant mass).
Newton’s 3rd Law: When body A exerts a force on body B, B exerts an equal and opposite force on A. These are interactions.
Free-Body Diagrams (FBDs): Essential diagrams showing all forces acting on a single body.

Types of Forces

Contact Forces	Field Forces
Normal force, Friction, Tension, Elastic restoring force, Viscous drag, Buoyancy.	Gravitational, Electric, Magnetic.

Important Formulas

F_{net} = ma

Newton's Second Law for constant mass.

p = mv

Linear momentum as the product of mass and velocity.

F = \dfrac{\Delta p}{\Delta t}

Resultant force as the rate of change of momentum.

J = F\Delta t = \Delta p

Impulse equals change in momentum (area under F-t graph).

F_f \le \mu_s R \, , \, F_f = \mu_k R

Static and dynamic friction equations.

a_c = \dfrac{v^2}{r} = \omega^2 r

Centripetal acceleration directed toward the center.

Collisions and Circular Motion

Elastic Collisions: Both momentum and Kinetic Energy (KE) are conserved.
Inelastic Collisions: Momentum is conserved, but KE is lost (usually to heat/sound).
Centripetal Force: A resultant force acting towards the center; it changes the direction of velocity but not the speed.

Practice Problems

Impulse and Momentum

A tennis ball of mass

0.06\ \mathrm{kg}

hits a wall at

15\ \mathrm{m\,s^{-1}}

and bounces back at

12\ \mathrm{m\,s^{-1}}.

Calculate the impulse exerted by the wall on the ball.

Friction on a level surface

A crate of mass

20\ \mathrm{kg}

is pulled by a horizontal force of

100\ \mathrm{N}.

If the coefficient of dynamic friction

\mu_k = 0.3

, find the acceleration (use

g = 9.8\ \mathrm{m\,s^{-2}}

Circular Motion

An object moves in a circle of radius

2.0\ \mathrm{m}

at a constant speed of

4.0\ \mathrm{m\,s^{-1}}.

Find the centripetal acceleration and describe its direction.

Clarity Tip: When dealing with collisions or explosions, always define a coordinate system (e.g., right is positive). Total momentum is conserved in any system where no external forces act.