Angular Acceleration

Figure 50.

Cranks exert torque on an object using a very long radius input or length input and a very short radius or length output, so that it can exert a significant torque on the system.

Pulleys will have a mechanical advantage of one per pulley but the force changes direction. The force will not change in magnitude as long as the pulleys are friction-free. The total force is an integral multiple of the tension on the cable. This means that two pulleys pulling a force will have two times the mechanical advantage applied to the weight.

ANGULAR ACCELERATION

Thus far, we have discussed uniform circular motion and gravitation, which is motion having a constant angular velocity at a constant speed. Recall that angular velocity omega is the change in angle theta divided by the change in time and that linear velocity is equal to the radius times the angular velocity. According to sign convention, counterclockwise angular velocity is considered positive and clockwise angular velocity is considered negative.

The angular velocity is not constant when the radius is changed, such as when a skater pulls in her arms or when a turntable is turned off. This causes something we haven’t talked about yet, which is angular acceleration or alpha. This is defined as the change in angular velocity divided by the change in time, given in units of radians per second