A disk with mass m = 10.6 kg and radius R = 0.36 m begins at rest and accelerate

Question

A disk with mass m = 10.6 kg and radius R = 0.36 m begins at rest and accelerates uniformly for t = 17.6 s, to a final angular speed of = 29 rad/s.

1. 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?

2. 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? 

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

4. What is the total distance a point on the rim of the disk travels during the 17.6 seconds? 

Explanation / Answer

(1) Angular acceleration, ? = ?? / ?t = 29 rad/s / 17.6s = 1.65 rad/s²

Tangential acceleration = a = ? r = 1.65rad/s² * 0.36m = 0.59 m/s²  

(2) Radial component of acceleration = a = ?² r = (29/2 rad/s)² * 0.36m = 75.7 m/s²

(3) Final speed = v = ? r = 29rad/s * ½(0.36m) = 5.22 m/s

(4)  ? = ½?t² = ½ * 1.65rad/s² * (17.6s)² = 255.6 rads

Total distance travelled by the point = s = ? r = 255.6 rads * 0.36m = 92 m

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