# Angular Acceleration (Grindstone Problem)

## Homework Statement

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?

(a) 0.313 rad/s2 (c) 2.50 rad/s2 (e) 3.93 rad/s2

(b) 0.625 rad/s2 (d) 1.97 rad/s2

## Homework Equations

Rotational Kinematic equations

## The Attempt at a Solution

Ok so I am using the equation ω = ω (initial) + ∝ T
BUT my answer is the wrong one. It seems that I have to use this equation ω^2 = ω (initial) ^2 + 2∝Θ
but what do I put in liew of "Θ"??????

I just don't understand why is that I have to use that equation?

## Answers and Replies

haruspex
Science Advisor
Homework Helper
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Ok so I am using the equation ω = ω (initial) + ∝ T
BUT my answer is the wrong one. It seems that I have to use this equation ω^2 = ω (initial) ^2 + 2∝Θ
but what do I put in liew of "Θ"??????
I don't see how you can use that equation directly since you don't know the final angular speed.
These equations for uniform angular acceleration are completely analogous to the SUVAT equations for uniform linear acceleration.
linear.......angular
distance......angle
speed..........angular speed
acceleration..angular acceleration
Given a distance, an initial speed and a time, what equation would you use to find the acceleration?

I don't see how you can use that equation directly since you don't know the final angular speed.
These equations for uniform angular acceleration are completely analogous to the SUVAT equations for uniform linear acceleration.
linear.......angular
distance......angle
speed..........angular speed
acceleration..angular acceleration
Given a distance, an initial speed and a time, what equation would you use to find the acceleration?
angular acceleration = change in angular velocity/time

=(final ang vel-initial ang vel)/time

here, initial ang vel =0
final ang vel = 20 rev/s = 125.6 rad/s (there are 2 pi radians/rev)

so, ang accel = (125.6rad/s)/8s=15.7rad/s/s or

I still don't have the answer!!!!

haruspex
Science Advisor
Homework Helper
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angular acceleration = change in angular velocity/time
Yes, but that's not what I asked. Forget this question and angular motion for the moment. In linear uniform acceleration,
Given a distance, an initial speed and a time, what equation would you use to find the acceleration?
I.e., what SUVAT equation relates distance, time, initial velocity, and acceleration?

Yes, but that's not what I asked. Forget this question and angular motion for the moment. In linear uniform acceleration,

I.e., what SUVAT equation relates distance, time, initial velocity, and acceleration?

θ = ω t + 1/2 t^2

that one

haruspex
Science Advisor
Homework Helper
Gold Member
θ = ω t + 1/2 t^2

that one
Yes (except that you missed out one symbol).