A disk with initial angular velocir+s yndergoes a constant angular acceleration

Question

A disk with initial angular velocir+s yndergoes a constant angular acceleration - Derive an expression for the angular displacement the disk travels in the CCW direction. Give your answer in terms of wo and a Part (b) 12 points isonfor the time it takesthedisktochargedirectiondjntermsofa%anda. se chosen kein to suites doth Changt in directen mens thors a charge in es pecenth Part (c) [1 point) Which of the following is true for a point a distance R away from the axis of rotation at the time the disk changes direction: Circle one: at = 0 v, 0) 0 CONTINUE ON NEXT PAGE

Explanation / Answer

a)

The angular acceleration is constant and hence the calculation goes as follows.

d (omega)/dt = - alpha * t

omega - omega_0 = -alpha *t

omega = omega_0 - alpha* t

where, omega is the angular velocity at time t and omega_0 is the initial angular velocity.

d(theta)/dt = omega_0 - alpha*t

Delta theta = omega_0 * t - 0.5 alpha * t^2

where 'Delta theta' is angular displacement.

Part b.

When disk changes its direction, the angular velocity will be zero hence,

omega = omega_0 - alpha*t

0 = omega_0 - alpha*t

t = omega_0/alpha

t is the time taken.

Part c.

When the disk changes its direction, the angular velocity is zero and hence the tangential component of the velocity will be zero.

vt = 0

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