Rotational Motion: Disc Movement

AI Thread Summary
The discussion focuses on calculating various properties of a grinding wheel in rotational motion, including its rotational inertia, initial angular velocity, angular acceleration, and torque due to friction. The user correctly identifies the rotational inertia of the wheel as 5.86 x 10^-2 kgm^2 and converts the initial angular velocity from 220 rpm to 23.04 rad/s. They attempt to find angular acceleration using linear motion equations but express confusion about whether the initial angular velocity should be 23.04 rad/s or 220 rpm. The user seeks clarification on their calculations and the correct interpretation of the variables involved. The thread emphasizes understanding the relationships between linear and angular motion in rotational dynamics.
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Homework Statement


A 750 gram grinding wheel 25.0 cm in diameter is in the shape of a uniform solid disc. When it is in use it turns at a constant 220 rpm about an axis perpendicular to its face through its center. When the power is switched off the wheel stops in 45.0 s with constant angular acceleration due to friction

A) What is rotational intertia of the wheel?
B) What is the initial angular velocity in rad/s?
C) What is the constant angular acceleration in rad/s^2?
D) What is the magnitude of the torque exerted by friction in N-m?

m = 0.750 kg
r= 0.125 m
wf = 23.04 rad/s (converting 220rpm)
t= 45.0 s

Homework Equations


Part A) Idisc= 0.5(mr^2) = 0.5(0.750kg)(0.125m^2) = 5.86*10^-2 kgm^2

The Attempt at a Solution



I was thinking along these lines... I could find part C first (angular acceleration - alpha) and use that to find part B (initial angular velocity - w0) by using this equation : wf = w0 + alpha(time). I could then find part D (torque - T) by using this equation : alpha = T/I

My problem is finding angular acceleration, or alpha.

This is what I did, please let me know if it's correct or not.

v(speed)= radius*wf
v = (0.125m)(23.04 rad/s) = 2.88
vf= v0 +a(linear)(time)
2.88 = 0 +a(45seconds)
a(linear) = 0.064 m/s
a(linear) = radius*a(angular)
0.064 = 0.125*a
alpha = 0.512 rad/s^2

If it's wrong, could you please advise on how to get the right answer?
Thank you in advance :)Disclaimers: This is my first post, so please be gentle! Also, this is not homework, it is a practice test. Thanks again!
 
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Did I read this wrong... I assumed wf= 220rpm = 23.04 rad/s. Is the 220rpm actually w0? And if so, am I just converting it wrong?
 
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