Angular motion: Application of Newton’s laws to angular motion.

The idea

Newton’s laws can be applied to rotating bodies. The first law states that a body continues in uniform rotational motion unless acted on by a net external torque; a spinning skater keeps rotating until friction or another torque slows them. The second law states that the net torque equals the rate of change of angular momentum, or torque equals moment of inertia multiplied by angular acceleration (τ = Iα). A larger torque or a smaller moment of inertia produces greater angular acceleration. The third law states that for every torque there is an equal and opposite torque on another body; a swimmer pushing water backwards experiences an equal and opposite torque from the water.

What earns the marks

• Newton’s first law applied to angular motion: a rotating body continues with constant angular velocity unless acted on by a net external torque.
• Newton’s second law applied to angular motion: net torque equals the rate of change of angular momentum, or τ = Iα.
• Torque is the rotational effect of a force and depends on the magnitude of the force and the perpendicular distance from the axis of rotation.
• Moment of inertia (I) is the resistance of a body to change in its angular motion and depends on mass distribution relative to the axis.
• Newton’s third law applied to angular motion: for every torque there is an equal and opposite torque on another body.
• Sporting examples include a gymnast rotating about a bar, a diver tucking to reduce moment of inertia, and a swimmer pushing water to generate torque.

Common mistakes and how to put them right

• Misunderstanding: Newton’s laws only apply to linear motion.

  Put it right: They also apply to angular motion when force is replaced by torque, mass by moment of inertia, and linear acceleration by angular acceleration.

• Misunderstanding: torque and force are the same thing.

  Put it right: Torque is the rotational effect of a force and depends on both the force and its perpendicular distance from the axis of rotation.

• Misunderstanding: moment of inertia is the same for all axes.

  Put it right: Moment of inertia depends on how mass is distributed relative to the axis of rotation, so it changes when a body changes shape.

• Misunderstanding: Newton’s third law does not apply to rotation.

  Put it right: For every torque there is an equal and opposite torque on another body, as when a swimmer pushes water backwards.

Exam tips

• When applying Newton’s second law to angular motion, state the equation τ = Iα and define each symbol.
• Use sporting examples to show how changing the moment of inertia affects angular acceleration, such as a diver tucking.
• Remember that torque depends on the perpendicular distance from the axis, so a force applied further from the axis produces a larger torque.
• Check that your units are consistent: torque in newton metres (N m), moment of inertia in kilogram metre squared (kg m²), and angular acceleration in radians per second squared (rad s⁻²).