A.4 Rigid body mechanics

What is torque?

The twisting effect of a force acting on object around a specific pivot point or axis

Torque formula

What does an unbalanced torque to an extended rigid body cause?

An angular acceleration.

List Linear and Angular SUVAT

s - displacement, Δθ - angular displacement

u - initial velocity, ω_i - initial angular velocity

v - final velocity, ω_f - final angular velocity

a - acceleration, α - angular acceleration

Couples

A pair of equal and opposite forces that do not act in the same straight line. This combination of forces produces a torque that causes an object to undergo angular acceleration but not translational acceleration (the object stays in place but will rotate on the spot).

When an object is not in equilibrium and is undergoing rotational motion what can be said about its angular speed, angular acceleration and torque?

• The angular speed is changing

• The angular acceleration is not 0

• 𝜏 = Iα

When an object is equilibrium and is undergoing rotational motion what can be said about its angular speed, angular acceleration and torque?

• The angular speed is constant

• The angular acceleration is 0.

• 𝜏 = 0

Moment of inertia formula

The moment of inertia depends on the distribution of mass of an extended body about an axis of rotation

Newton’s second law for rotation

τ = Iα where τ is the average torque

Angular momentum formula

Angular momentum remains constant unless the body is acted upon by a resultant torque

Angular impulse formula (angular change in momentum)

ΔL = τΔt = Δ(Iω)

Rotational Kinetic Energy Formula