Angular Acceleration (Grindstone Problem)

AI Thread Summary
A grindstone is initially at rest and experiences constant angular acceleration, completing 20 revolutions in 8 seconds. To find the angular acceleration, the relevant rotational kinematic equations must be applied. The discussion highlights confusion regarding which equation to use, particularly between ω = ω(initial) + αT and ω² = ω(initial)² + 2αΘ. Participants emphasize the need to relate angular displacement (Θ) to the given revolutions and time. Ultimately, the correct approach involves using the equation θ = ωt + 1/2αt² to solve for angular acceleration.
gcombina
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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?
 
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gcombina said:
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?
 
haruspex said:
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!
 
gcombina said:
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,
haruspex said:
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?
 
haruspex said:
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
 
gcombina said:
θ = ω t + 1/2 t^2

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