Which Equation Determines Angular Displacement for a Rotating Pulley Wheel?

[lubo]

Homework Statement

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

Homework Equations

θ=Wo*t+1/2*\alpha*t squared

θ=(Wo+W)/2)*t

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.

 

[Doc Al]

Wo (inital angular velocity) = 6Rad/s

OK.

W (angular Velocity) = 0 Rads/s

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

θ=Wo*t+1/2*\alpha*(t squared)

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

That's fine.

or θ=(6+0)/2)*10 = 30 Rads.

You are using W = 0, which is incorrect.

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.

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.

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.

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