# 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?
in rad/s2

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

i got the answers: 6.3 seconds and -3.17 rad/s^2

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