# Angular Displacement and Velocity

1. Feb 5, 2009

### Bigdane

1. The problem statement, all variables and given/known data
A person is riding a bicycle, and its wheels have an angular velocity of +22.0 rad/s. Then, the brakes are applied and the bike is brought to a uniform stop. During braking, the angular displacement of each wheel is +11.0 revolutions.

(a) How much time does it take for the bike to come to rest?
s

(b) What is the angular acceleration of each wheel?

2. Relevant equations
theta = (angular velocity)(time)

3. The attempt at a solution
11=22t
11/22 = t=1/2

thats wrong i guess.
can you help me out?

2. Feb 5, 2009

### AEM

Here's an interesting thing: The kinematic equations for rotational motion (be sure to use radians) have the same form as those for straight line motion:

$$X = X_o + V_o t + \frac{1}{2} a t^2$$

becomes

$$\theta = \theta_o + \omega_o t + \frac{1}{2} \alpha t^2$$

and so on. Therefore you can use many of the same ideas that you would use for straight line motion problems with simple rotational kinematics. For example, you could use

$$\omega^2 = \omega_o^2 + 2 \alpha(\theta - \theta_o)$$

to find the angular acceleration in your problem above. I'll leave it to you to figure out the other parts.

$$\omega$$ is the angular velocity; $$\alpha$$ is the angular acceleration in the above equations.