A disk with mass m = 9.1 kg and radius R = 0.38 m begins at rest and accelerates

Question

A disk with mass m = 9.1 kg and radius R = 0.38 m begins at rest and accelerates uniformly for t = 17.1 s, to a final angular speed of omega = 34 rad/s. What is the angular acceleration of the disk? What is the angular displacement over the 17.1 s? What it the moment of inertia of the disk? What is the change in rotational energy of the disk? 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? 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? What is the final speed of a point on the disk half-way between the center of the disk and the rim? What is the total distance a point on the rim of the disk travels during the 17.1 seconds? Below is some space to write notes on this problem

Explanation / Answer

m = 9.1 kg. , R = 0.38 m, w0 = 0, t = 17.1 s, w = 34 rad/s.

(1) Angular acceleration, alfa = (delta) w / (delta) t = 34/17.1 = 1.99 rad/s^2

(2) Angular displacement, theta = (1/2)*alfa*t^2 = 0.5*1.99*17.1^2 = 291 rad.

(3) Moment of Inertia of the disc, I = (1/2)m*R^2 = 0.5*9.1*0.38^2 = 0.66 kg-m^2

(4) Change in rotational energy of the disk, deltaEk = (1/2)*I*w^2 = 0.5*0.66*34^2 = 381.5 J

(5) Tangential component of acceleration, a = alfa*R = 1.99*0.38 = 0.77 m/s^2

(6) Radial component of acceleration, a = w^2*R = 17^2*0.38 = 110 m/s^2

(7) v = w*R = 34*(0.38/2) = 6.46 m/s

(8) s = theta*R = 291*0.38 = 110.6 m

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