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A disk with mass m = 11.8 kg and radius R = 0.31 m begins at rest and accelerate

ID: 1912923 • Letter: A

Question

A disk with mass m = 11.8 kg and radius R = 0.31 m begins at rest and accelerates uniformly for t = 17.2 s, to a final angular speed of ? = 31.0 rad/s.

1) What is the angular acceleration of the disk? rad/s2

2) What is the angular displacement over the 17.2 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 17.2 seconds? m

A disk with mass m = 11.8 kg and radius R = 0.31 m begins at rest and accelerates uniformly for t = 17.2 s, to a final angular speed of ? = 31.0 rad/s. 1) What is the angular acceleration of the disk? rad/s2 2) What is the angular displacement over the 17.2 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 17.2 seconds? m

Explanation / Answer

w2=t==>= 31/17.2= 1.8

b)w^2=2s==>s= 266.9

c)I=mr^2/2 =0.566

d)1/2Iw^2= 0.916

e)a=v^2/r =rw^2 =0.31*1.8^21.004

f)r1w1=r2w2==> 2*1.8=3.6

g)w^2=2s==>s= 266.9 266.9*2*3.14*0.31= 519.6

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