11.1.4 Torque and angular acceleration

Torque

Torque $( T )$ is the product of a force $( F )$ and its distance from the axis of rotation $( r )$. Torque is responsible for causing rotation and is measured in newton-metres ($Nm$).

The equation for torque is:

$$T = F \times r$$

Where:

• $T$ = Torque
• $F$ = Force applied
• $r$ = Distance from the axis of rotation

Explanation of Torque

The concept of torque can be visualised with a wheel and axle setup:

• When a mass is attached to the axle, it exerts a force at a distance from the centre. This force generates torque, leading to angular acceleration in the wheel.

Increasing Angular Acceleration

The angular acceleration of an object can be increased by:

• Increasing the mass ($m$), which increases the torque.
• Using a lighter wheel, reducing the moment of inertia, making it easier to accelerate.

Torque, Inertia, and Angular Acceleration Relationship

The relationship between torque $( T )$, moment of inertia ($$ I ), and angular acceleration $( \alpha )$ is given by:

$$T = I \alpha$$

Where:

• $T$ = Torque
• $I$ = Moment of inertia, a measure of how much an object resists rotational acceleration
• $\alpha$ = Angular acceleration

This equation is analogous to Newton's second law $( F = ma )$ for linear motion, where force results in acceleration. Here, torque results in angular acceleration.