# Angular speed and acceleration

1. Oct 20, 2006

### 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?

2. Oct 20, 2006

### Staff: Mentor

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

3. Oct 20, 2006

### physics1234

What would be the best way to do it then?

4. Oct 20, 2006

### Staff: Mentor

Tell me the definition of acceleration.

5. Oct 20, 2006

### physics1234

acceleration

The changing of an object's velocity with time.

6. Oct 20, 2006

### OlderDan

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.

7. Oct 20, 2006

### Staff: Mentor

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.)