# Pulley wheel rotation question

1. Dec 19, 2011

### lubo

1. The problem statement, all variables and given/known data
A solid pulley wheel is rotated at a constant velocity for 10 sec's. Find the angular displacement?

Wo (inital angular velocity) = 6Rad/s
W (angular Velocity) = 0 Rads/s
$\alpha$ = 0 (angular acceleration) Rads/s-2
θ = ? (angular displacement) Rads/s
t = 10 sec

2. Relevant equations

θ=Wo*t+1/2*$\alpha$*t squared

θ=(Wo+W)/2)*t

3. The attempt at a solution

θ=Wo*t+1/2*$\alpha$*(t squared)

displacement θ = 6 * 10 + 1/2 * 0 * t = 60 Rads

or θ=(6+0)/2)*10 = 30 Rads.

I cannot tell which one is right as they both should find θ. All I know is that there is an angular acceleration of 0 and 60 is the right answer. Does this mean I have to use an equation with $\alpha$ in it?

I thought I could use anyone I liked as it found θ.

Another example is if I decelerate:

Wo = 6 Rads
$\alpha$ =-3Rads
t = 2 sec

θ=Wo*t+1/2*$\alpha$*t squared

displacement θ = 6 * 2 + 1/2 * -3 * (2^2) = 6 Rads

or θ=(6+0)/2)*2 = 6 Rads.

Why would this work out or is it just luck? I know the answer to be 6 Rads.

Thank you for any help in advance.

2. Dec 19, 2011

### Staff: Mentor

OK.
I thought the speed was constant? W = 6 rad/s.

That's fine.

You are using W = 0, which is incorrect.

You can use either one. (Of course, all you really need is θ = ωt, since the speed is constant.) But you have to use the right values.

A little bit of luck. You assumed that the final velocity ω equaled 0 at t = 2 sec. Happens to be true.