A coin with a diameter of 2.45 cm is dropped on edge onto a horizontal surface. The coin starts out with an in

Question

A coin with a diameter of 2.45 cm is dropped on edge onto a horizontal surface. The coin starts out with an initial angular speed of 21.8 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular acceleration of magnitude how far does the coin roll before coming to rest?

Answer 1

The formulas for angular motion are exactly parallel to those for linear motion. The formula for angular velocity under constant acceleration is:

Wf = Wi + A x T

In this case, you know Wi (the initial angular velocity), Wf (the final velocity, 0 when the coin stops), and the angular acceleration, so you can compute the time T.

The formula for angular distance (in radians) is:

D = Wi x T + (1/2) x A x T^2

If the coin rolls without slipping, then an angular displacement of D radians corresponds to a linear distance of D x R where R is the radius.