Grindstone angular acceleration

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SUMMARY

The discussion focuses on calculating the angular acceleration of a disk-shaped grindstone with a mass of 1.69 kg and a radius of 7.95 cm, initially rotating at 707 revolutions per minute (rev/min). The grindstone takes 32.1 seconds to stop after power is cut off. The correct approach involves converting the initial angular velocity (Wo) from rev/min to radians per second and applying the equation for angular motion, leading to an angular acceleration (a) of -0.140 rad/s². The initial calculations presented were incorrect due to misapplication of energy equations instead of rotational motion equations.

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[SOLVED] Grindstone angular acceleration

Homework Statement


Object: a disk-shaped grindstone of mass 1.69 kg and radius 7.95 cm that operates at 707 rev/min. When the power is shut off, you time the grindstone and find it takes 32.1 s for it to stop rotating. What is the angular acceleration of the grindstone? (Assume constant angular acceleration.)

Homework Equations


W=.5mv^2
V=distance/t
W=Wo+at
a=alpha, which is angular acceleration

The Attempt at a Solution


V=[707*(2pi/60)]/32.1 = 2.31m/s
W=0
Wo=.5(1.69)(4.50^2) = 4.50J
0=4.50+a(32.1)
therefore, a=-.140 rad/s^2

however, this is the wrong answer according to the program. It didn't have a problem with the units though, so I don't know what I am doing wrong. Please point out any wrong assumptions or completely wrong or silly mistakes. THANK YOU!
 
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You seem to have W representing two different things here. I don't know what you are trying to do with the first equation you have, but it's not for rotational motion. Also, Wo is your initial angular velocity, I don't understand why you are trying to make it into energy?:confused:

All you need for this is your third equation. Change the 707 rev/min into rad/s, that is your Wo. Solve for the angular acceleration.
 

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