Torque and Rotational Dynamics

So far we have studied objects moving in circles. Now we turn to objects that rotate — spinning about an axis. The physics of rotation mirrors the physics of linear motion, but with angular quantities replacing linear ones.

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Torque

You already know that a moment is force × perpendicular distance from the pivot. A torque (or the torque of a couple) specifically refers to a pair of equal and opposite forces that cause rotation without translation.

For a single force at perpendicular distance d from the axis of rotation:

$\tau = Fd$τ=Fd

Where τ (Greek letter tau) is the torque, measured in N m.

More generally, if the force is at angle θ to the line joining the point of application to the axis:

$\tau = Fr\sin\theta$τ=Frsinθ

Couples

A couple consists of two equal and opposite forces separated by a distance d. The torque of a couple is:

$\tau = Fd$τ=Fd

where F is the magnitude of one of the forces and d is the perpendicular distance between them. A couple produces pure rotation with no net translational force.

Worked Example 1