Angular impulse

A torque applied for a while is what changes a rotation. EK 6.3.B.1 defines angular impulse as the product of the torque exerted on an object or rigid system and the time interval during which the torque is exerted. The AP Physics 1 equation sheet prints the result:

Units are $\text{N}\cdot\text{m}\cdot\text{s}$, the same combination as $\text{kg}\cdot\text{m}^2/\text{s}$, because angular impulse and angular momentum are the same kind of quantity.

It is the rotational twin of [impulse](/glossary/impulse). Linear impulse $F_{\text{avg}}\Delta t$ changes momentum; angular impulse changes angular momentum. The two statements have the same structure, and remembering one gives you the other.

The graph rule carries over. EK 6.3.B.3 says the angular impulse delivered by a torque can be found from the area under a graph of torque against time, which is what you use when the torque is not constant.

It has the direction of the torque. EK 6.3.B.2. At AP Physics 1 that means it carries the sign of whichever sense of rotation you declared positive.

The consequence that gets tested: with no net external torque the angular impulse is zero, so angular momentum is conserved. That is the skater pulling her arms in, where the rotational inertia drops and the angular velocity rises to keep $I\omega$ fixed. Her kinetic energy is not conserved there; it rises, paid for by the work she does pulling her arms in.