# What is the angular acceleration of each wheel?

1. Nov 23, 2007

### rcmango

1. The problem statement, all variables and given/known data

A person is riding a bicycle, and its wheels have an angular velocity of +20.0 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 +10.0 revolutions.

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

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

2. Relevant equations

3. The attempt at a solution

what is the symbol of a revolution. Can i use a kinematic equation for this.

2. Nov 23, 2007

### rock.freak667

hm..angular displacement.$\theta$ is related to angular velocity,$\omega$
by the equation:

$$\omega=\frac{\theta}{t}$$

where t is time

3. Nov 23, 2007

### rcmango

okay, so if i manipulate the formula to look like t = theta / w

then the time is .5 seconds, however, that is not correct?

4. Nov 23, 2007

### azatkgz

a)for the first one use kinematics formula

$$x=\frac{(v_0+v_f)}{2}t$$

so we have
$$\theta=\frac{(\omega_0+\omega_f)}{2}t$$

b)$$\alpha=\frac{d\omega}{dt}=\frac{d\omega}{dt}\frac{d\theta}{d\theta}$$

$$\alpha d\theta=\omega d\omega$$

$$\alpha\theta=\frac{\omega^2}{2}$$

5. Nov 23, 2007

### rcmango

for the first one, 1 second isn't the anwer and i'm not sure why

i used 10 rev = (+20 - 0)/2 t

so 1 second??

also, for the second one

20^2 = 400

so 400/2

=200
and that is not correct either.

i'm not sure what i did wrong.

Last edited: Nov 23, 2007
6. Nov 24, 2007

### hotcommodity

You're mixing revolutions with radians, you'll have to convert units to one or the other.

7. Nov 24, 2007

### rcmango

thanks, that fixed it, i didn't realise that 1 revolution is actually convert to 2 * pi radians