A disk with mass m = 8.4 kg and radius R = 0.34 m begins at rest and accelerates

Question

A disk with mass m = 8.4 kg and radius R = 0.34 m begins at rest and accelerates uniformly for t = 18.6 s, to a final angular speed of = 27 rad/s.

1)

What is the angular acceleration of the disk?  

rad/s2

2)

What is the angular displacement over the 18.6 s?

rad

3)

What is the moment of inertia of the disk?

kg-m2

4)

What is the change in rotational energy of the disk?

J

5)

What is the tangential component of the acceleration of a point on the rim of the disk when the disk has accelerated to half its final angular speed?  

m/s2

6)

What is the magnitude of the radial component of the acceleration of a point on the rim of the disk when the disk has accelerated to half its final angular speed?  

m/s2

7)

What is the final speed of a point on the disk half-way between the center of the disk and the rim?  

m/s

8)

What is the total distance a point on the rim of the disk travels during the 18.6 seconds?  

m

Explanation / Answer

1) alpha = wf-wi/t = 27/18.6 = 1.45 rad/s^2

2) theta = 1/2*alpha*t^2 = 251.1 rad

3) I = 1/2mr^2 = 0.485 kg m^2

4) k =1/2Iw^2 = 176.9 J

5) alpha = 27/2*18.6 = 0.725 rad/s^2

a = r*alpha = 0.247 m/s^2

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