Rotational Motion: Disc Movement

[kikidoll]

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!

 

[kikidoll]

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?

 

[nlightner]

Hello! I would like to provide a response to your content on rotational motion and disc movement.

Firstly, I would like to commend you on your attempt at finding the answers to the given questions. Your method of finding the angular acceleration, or alpha, is correct. However, there is a small calculation error in your solution. The correct value for alpha is 0.045 rad/s^2, as you have correctly calculated the linear acceleration to be 0.064 m/s^2, but you forgot to divide it by the radius.

Moving on to the questions, I would like to provide the following responses:

A) The rotational inertia of the wheel, or Idisc, can be calculated using the formula Idisc= 0.5mr^2, where m is the mass of the wheel and r is the radius. Plugging in the given values, we get Idisc= 5.86*10^-2 kgm^2.

B) The initial angular velocity, or w0, can be found using the equation wf= w0 + alpha(time). Plugging in the values, we get w0= 23.04- (0.045)(45)= 20.94 rad/s.

C) The constant angular acceleration, or alpha, can be found using the equation alpha= a(linear)/r. Plugging in the values, we get alpha= 0.064/0.125= 0.512 rad/s^2.

D) The magnitude of the torque exerted by friction, or T, can be found using the equation alpha= T/Idisc. Plugging in the values, we get T= (0.045)(5.86*10^-2)= 0.00264 N-m.

I hope this helps and clarifies any doubts you may have had. Keep up the good work!