# Angular Acceleration (p.20)

1. Oct 21, 2014

### gcombina

1. The problem statement, all variables and given/known data
A grindstone, initially at rest, is given a constant angular acceleration so that it makes 20.0 rev in the first 8.00 s. What is its angular acceleration?

2. Relevant equations

3. The attempt at a solution

#1. I am changing the rev part to radians

20rev = 125.66

#2. I am using the formula

w^2 = w^2 + 2 alpha tetha (where are the symbols????)

2. Oct 21, 2014

### Dr.D

What do you mean when you write

"w^2 = w^2 + 2 alpha tetha "

If we subtract w^2 from both sides, doesn't this leave you with 2 alpha tetha = ? Where did you get that last formula?

By the way, I think you most likely mean theta, rather than tetha.

3. Oct 22, 2014

### gcombina

The equation you used relates the acceleration, displacement, initial and final velocities, and leaves out the time. If the question asked to find the angular acceleration given : that the wheel starts from rest (ωo = 0), and reaches a velocity of ωf rad/sec when it is stopped after making Θ number of revolutions, you would use ω^2 - ωo^2 = 2∝ Θ
The equation you want is the one that includes the time t.
***** Θ = Vo t + 1/2 (∝) (t^2) ******

Θ = 20 rev x (2 pi rad/ rev) = 125.6 tad

125.6 = 0 + 0.5 (or 1/2) ∝ (8)^2 and
∝ = 125.6/32