A disk with mass m = 8.2 kg and radius R = 0.33 m begins at rest and accelerates

Question

A disk with mass m = 8.2 kg and radius R = 0.33 m begins at rest and accelerates uniformly for t = 18.1 s, to a final angular speed of = 25 rad/s.

1)

What is the angular acceleration of the disk?  

rad/s2

2)

What is the angular displacement over the 18.1 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 18.1 seconds?  

m

Explanation / Answer

1. = / t = 25 rad/s / 18.1s = 1.38 rad/s²

2. = ½t² = ½ * 1.38rad/s² * (18.1s)² = 226.05 rads

3. I = ½mr² = ½ * 8.2kg * (0.33m)² = 0.446 kg·m²

4. Ek = ½I² = ½ * 0.44kg·m² * (25rad/s)² = 137.5 J

5. a = r = 1.38rad/s² * 0.33m = 0.45 m/s²

6. a = ² r = (12.5rad/s)² * 0.33m =51.56 m/s²

7. v = r = 25rad/s * ½(0.33m) = 4.12 m/s

8. s = r = 226.05 rads * 0.33m = 74.55 m

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