A ball attached to the end of a string is swung around in a circular path of radius r.If the radius is doubled and the linear speed is held constant,the angular speed will
A)remain the same.
B)increase by a factor of 2.
C)decrease by a factor of 2.
D)increase by a factor of 4.
E)decrease by a factor of 4.

Question

Quizplus · Accepted Answer

Angular speed is inversely proportional to the radius of the circular path. When the radius is doubled, the angular velocity reduces by a factor of 2 to maintain the same linear speed. This can be derived from the formula: v = rω, where v is the linear speed, r is the radius, and ω is the angular speed. Maintaining v constant requires ω to reduce by half when r is doubled.

A Ball Attached to the End of a String Is