Angular Velocity and Acceleration - Examples

Angular Velocity and Acceleration

An airplane propellor turns at a constant rate of 3000 revolutions per minute. Find its angular velocity in radians per second.

Angle turned through in one minute
= (3000rev)= (3000)(2rad) = 6000rad

= (6000rad)/(60s) = 100rad/s
= 314rad/s

Examples --- What this is an example of

An airplane propellor spins up from zero to 3000rpm (314rad/s) in ten seconds. What is its angular acceleration in rad/s?

= (314rad/s - 0)/(10s) = 31.4rad/s.

Examples --- What this is an example of

A model airplane flys in a circle with a radius of 10 meters. It circles once every ten seconds. Find its speed relative to the ground.

First calculate the angular velocity in rad/s.

= (2rad)/(10s) = 0.628rad/s.

Next, use the relationship between angular and linear velocity:

v = (10m)(0.628rad/s) = 6.28m/s.

Examples --- What this is an example of

A diver is suspended at the end of a long rope which is wound around a drum of radius 0.5m. The drum is turned by a motor which spins up from zero to 6rad/s (about one rev/s) in one second. Calculate the initial upward acceleration of the diver.

The acceleration of the rope in its direction of motion is the same all along its length. Calculate the acceleration where the rope is on the drum by using the formula:

= (0.5m)(6rad/s) = 3m/s.

A yo-yo is supported by a string which is wound around its central post. The string unwinds as the yo-yo descends. If the radius of the central post is half a centimeter (0.005m) and the yo-yo is accelerating downward at 1m/s, what is the angular acceleration of the yo-yo around its central post?

Use the relation

and solve it for .
= (1m/s)/(0.005m) = 200rad/s.

Examples --- What this is an example of