What is the angular acceleration of each wheel?

[rcmango]

Homework Statement

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

Homework Equations

The Attempt at a Solution

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

 

[rock.freak667]

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


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




where t is time

 

[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?

 

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

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

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

 

[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.

 

[hotcommodity]

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

 

[rcmango]

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

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