A disk with mass m = 11.5 kg and radius R = 0.3 m begins at rest and accelerates

Question

A disk with mass m = 11.5 kg and radius R = 0.3 m begins at rest and accelerates uniformly for t = 16.6 s, to a final angular speed of w = 28 rad/s. What is the angular acceleration of the disk? What is the angular displacement over the 16.6 s? What is 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 16.6 seconds?

Explanation / Answer

here,

mass of disk, md = 11.5 kg
radius , r = 0.3 m
time, t = 16.6 s
Final angular speed, w = 28 rad/s

Part A:
Angular acceleration, alpha = w^2*r = 28^2*0.3 = 235.2 rad/s^2

Part B:
from Second erqn of motion,
Angular displacement, theta = 0 + 0.5*alpha*t^2
Theta = 0.5 * 235.2 * 16.6^2
Theta = 32405.856 radians

Part C:
Moment of inertia of disk, I = 0.5*mr^2 = 0.5 * 11.5 * 0.3^2 = 0.5175 kg.m^2

Part D:
Change of rotatinal Energy, E = Efinal - Einitial = 0.5*I(Wf^2 - Wi^2)

E = 0.5*I*wf^2 = 0.5 * 0.5175 * 28^2 = 202.86 J

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