How Far Does a Coin Roll Before Stopping Given Its Angular Deceleration?

[physics1234]

A coin with a diameter of 2.20 cm is dropped on edge onto a horizontal surface. The coin starts out with an initial angular speed of 15.9 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular acceleration of magnitude 1.76 rad/s2, how far does the coin roll before coming to rest?

Ok, I figured out that the radius is 0.011m and then got stuck. How can you find distance without time?

 

[Doc Al]

You don't need to find the time, but you could find it using the definition of acceleration.

 

[physics1234]

What would be the best way to do it then?

 

[Doc Al]

Tell me the definition of acceleration.

 

[physics1234]

acceleration

The changing of an object's velocity with time.

 

[OlderDan]

The changing of an object's velocity with time.

In this problem you are given an initial angular velocity and angular acceleration. You know the final angular velocity is zero. You can find the angular diplacement and use that to find the distance the coin rolls. The angular equations are directly analogous to the linear equations.

 

[Doc Al]

The changing of an object's velocity with time.

Right, acceleration is the rate of change of velocity; analogously, angular acceleration is the rate of change of angular velocity. Now express that mathematically:
$$\alpha = \Delta \omega / \Delta t$$

You can use that to find the time. (You can also make use of any other kinematic relationships you know.)