A.2 Forces and momentum

UNIT SYLLABUS

SL/HL

Study of Newton's laws, conservation of momentum, and the relationship between force and motion.

1 Key Formulas

Newton's Second Law

F = \frac{\Delta p}{\Delta t} = ma

Static Friction

F_f \le \mu_s F_N

Dynamic Friction

F_f = \mu_d F_N

Hooke's Law

F_H = -kx

Linear Momentum

p = mv

Impulse

J = F\Delta t = \Delta p

Angular Velocity

\omega = \frac{2\pi}{T} = 2\pi f

Linear Speed

v = \omega r

Centripetal Acceleration

a = \frac{v^2}{r} = \omega^2 r = \frac{4\pi^2 r}{T^2}

Centripetal Force

F = m\frac{v^2}{r} = m\omega^2 r

2 Exam Preparation & Topic Explanations

Mastering Free-Body Diagrams & Forces

Free-body diagrams represent all forces acting on a body as vectors to find the resultant force.

Key concepts:

Equilibrium: A body will remain at rest or moving with constant velocity unless acted upon by an unbalanced force.

Inclined Planes: The weight is resolved into components: $mg \sin\theta$ parallel to the slope and $mg \cos\theta$ perpendicular to the slope.

Newton's Third Law: When body A exerts a force on body B, body B will exert an equal and opposite force of the same type on body A.

Pro Exam Strategy

Always draw a free-body diagram treating the object as a point mass.
Ensure you use consistent sign conventions when adding forces.
Remember that the normal reaction force is not always equal to the weight, especially on inclined planes.

Analyzing Collisions and Impulse

Momentum ( $p = mv$ ) is the product of mass and velocity, making it a vector quantity.

Key concepts:

Impulse: A resultant external force applied to a system constitutes an impulse, which is equal to the change in momentum.

Elastic Collisions: Both total momentum and total kinetic energy are conserved.

Inelastic Collisions: Total momentum is conserved, but kinetic energy is lost to forms like heat or sound. In a totally inelastic collision, the bodies stick together.

Explosions: Momentum is conserved, and kinetic energy is gained from the release of chemical or potential energy.

Pro Exam Strategy

Define a positive direction and stick to it, remembering that velocity and momentum are vectors.
The applied impulse equals the change in momentum of the system ( $J = \Delta p$ ).
When an object bounces, the change in momentum and the impulse are greater than if it simply comes to a stop without bouncing.

Mastering Circular Motion

Circular motion occurs when a resultant force continuously acts perpendicular to the velocity of an object, directing it towards the center of the circular path.

Key concepts:

Centripetal Force: This is not a new force, but the resultant force required to keep an object in circular motion. It can be provided by tension, friction, gravity, or normal reaction.

Angular Velocity ( $\omega$ ): Measured in radians per second, it represents the angle swept out per unit time.

Vertical Circular Motion: The required centripetal force equation changes depending on the position. At the top of a loop, gravity and normal force act downwards. At the bottom, normal force acts upwards while gravity acts downwards.

Pro Exam Strategy

Always identify the physical forces providing the centripetal force, such as friction for a car on a track.
Remember to measure angles in radians when using angular velocity equations.
Centripetal force does zero work because it is always perpendicular to the direction of instantaneous displacement.

3 MCQ Practice

Q1. According to Newton's second law, which of the following is correct for a situation where the mass of the system is changing?

$F = ma$
$F = \frac{\Delta p}{\Delta t}$
$F = p\Delta t$
$F = \frac{1}{2}mv^2$

Q2. In a totally inelastic collision between two bodies, which of the following is true?

Both momentum and kinetic energy are conserved.
Momentum is conserved, but kinetic energy is not conserved, and the bodies stick together.
Kinetic energy is conserved, but momentum is not.
Neither momentum nor kinetic energy are conserved.

Q3. A body moves in a horizontal circle at a constant speed. Which of the following statements about its acceleration is correct?

The acceleration is zero because the speed is constant.
The acceleration is directed tangentially to the circular path.
The acceleration is directed radially towards the center of the circle.
The acceleration is directed radially outwards from the center.

4 Short Answer Questions

Formula Booklet →

Every data-booklet equation, searchable.

Simulations →

See this physics in motion.

Daily Question →

Practise one concept a day.

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A.3 Work, energy and power

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