# Wheel rotation, constant acceleration

1. Nov 6, 2009

### matt3D

1. The problem statement, all variables and given/known data
A wheel rotates with a constant angular acceleration of 3.71 rad/s2.
what angle does the wheel rotate between t = 2.00 s and t = 6.25 s?

2. Relevant equations

$$\omega=\omega_{i}+\frac{1}{2}\alpha t^{2}$$
Δθ = θf - θi = ωit + αt2
3. The attempt at a solution
I found the angular speed at 2 seconds which is 10.01 rad/s.
Then I use the second equation:
$$\Delta\theta=10.01(6.25)+\frac{1}{2}(3.71)(6.25)^{2}=135.023 rads$$
I can't get the correct answer. What am I doing wrong?
Thanks,
Matthew

2. Nov 6, 2009

### willem2

The first equation you give is incorrect. It should be $\omega = \omega_i + \alpha t$, so your angular speed at 2 seconds is wrong.

The second equation should have $\Delta t$ in it instead of t, and also (1/2) inf front of the $\alpha$

3. Nov 6, 2009

### matt3D

Oops, yep, I didn't correctly enter the equations. Thanks willem2, I didn't know I needed the change in t for the second equation. I got 76.0484 rads for the angular rotation between t=2s and t=6.25s.

4. Nov 6, 2009

5. Nov 6, 2009

6. Nov 6, 2009

### matt3D

Sure, I did this:
Angular speed at 2s:
$$\omega= \omega_{i}+\alpha t \Rightarrow 2.59 rad/s + (3.71 rad/s2)(2.00 s)=10.01 rad/s$$
Then the change in t is 4.25s so:
$$\Delta\theta=10.01rad/s(4.25s)+\frac{1}{2}(3.71rad/s^{2})(4.25s)^{ 2}=76.0484 rads$$
Regards,
Matthew

7. Nov 6, 2009

### rl.bhat

From where did you get ωi = 2.59 rad/s?

8. Nov 6, 2009

### matt3D

Oh, I'm sorry, I forgot that the question stated that at $$t=0, \omega_{i}=2.59rad/s$$

9. Nov 6, 2009