Pulleys transfer torque, power and speed. Open the bonnet of your car and you'll find at least one belted pulley transferring the power of the engine to various accessories. Rim speed, or tangential velocity, is an expression of the speed being transferred by one pulley to another pulley -- in the case of the belted pulleys in your car -- or to a line in the case of fixed and movable pulleys. You can easily calculate the tangential velocity of a pulley if you know its radius and rate of rotation.
Determine how many complete revolutions the pulley makes in one minute. For example, a pulley makes 120 revolutions per minute.
Divide the number of pulley revolutions per minute by 60. In the example, 120/60 = 2. The pulley makes two revolutions per second. This is the pulley's frequency in seconds.
Multiply the frequency of the pulley by 2pi. Pi equals approximately 3.14. In the example, 2 x 2 x 3.14 = 12.56. The angular velocity of the pulley is 12.56 radians per second.
Measure the distance from the centre, or axis, of the pulley to the pulley rim. In the example, this distance is six centimetres.
Multiply the angular velocity of the pulley by the distance from the centre of the pulley to the rim. In the example, 12.56 x 6 = 75.36. The tangential velocity, or rim speed, of the pulley is 75.36 centimetres per second.