Rotational motion and torque
Rotational motion is described with quantities that mirror straight-line motion: angular displacement (how far an object has turned, often measured in radians), angular velocity (how fast it turns), and angular acceleration (how quickly its rate of turning changes). On a spinning object, a point farther from the axis moves faster: its linear speed equals its distance from the axis times the angular velocity (v = r x angular velocity). What starts or stops an object's rotation is torque, the turning effect of a force. Torque depends on the size of the force, how far from the pivot it is applied (the lever arm), and its direction: for a force applied perpendicular to the lever arm, torque = force x distance. That is why a door is easier to open when you push far from its hinges, and why a longer wrench loosens a stuck bolt more easily. An object is in rotational equilibrium when the torques on it balance, as on a seesaw where a lighter child sitting farther from the pivot balances a heavier child sitting closer in. For an object to be in complete equilibrium, both the net force and the net torque on it must be zero.
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