Rotational Dynamics

This lesson covers the equations of rotational motion — the rotational analogues of Newton's laws. This includes torque, angular acceleration, and the rotational analogues of the SUVAT equations.

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1 Newton's Second Law for Rotation

The rotational analogue of $F = ma$F=ma is:

$$\boxed{\tau = I\alpha}$$τ=Iα​

where:

• $\tau$τ = resultant torque (moment) about the axis of rotation (N m),
• $I$I = moment of inertia about the axis (kg m$^2$2),
• $\alpha$α = angular acceleration (rad s$^{-2}$−2).

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2 Torque

The torque (or moment) of a force $F$F about an axis is:

$$\tau = Fr$$τ=Fr

where $r$r is the perpendicular distance from the axis to the line of action of the force. More generally:

$$\tau = Fr\sin\theta$$τ=Frsinθ

where $\theta$θ is the angle between $\mathbf{F}$F and the position vector $\mathbf{r}$r.

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3 Rotational SUVAT Equations

When angular acceleration $\alpha$α is constant: