A disk with mass M= 10 kg and radius 50 cm is accelerated by a constant force F

Question

A disk with mass M= 10 kg and radius 50 cm is accelerated by a constant force F as shown in the figure.

What is the angular acceleration of the disk, if the initial speed of the disk was -2 rad/s and the speed after .5 seconds was +2 rad/s.

a) 8 rad/s^2

b) 4 rad/s^2

c) 2 rad/s^2

d) 0 rad/s^2

e) -8 rad/s^2

What was the change in kinetic energy of the of the same disk in .5 seconds?

What was the initial angular momentum of the disk?

a) 0 kg * m/s^2

b) 5 kg * m/s^2

c) -5 kg * m/s^2

d) 2.5 kg * m/s^2

e) -2.5 kg * m/s^2

Please explain answers

Explanation / Answer

Part-1

Angular acceleration = change in angular velocity/time taken
=>= [2-(-2)]/0.5 = 8rad/s^2

Part-2

Kinetice Energy = 1/2Mv^2

V= w*R

initial V = -2*1/2 m/s = -1m/s (50 cm = 1/2 m)

Final V = 2*1/2 = 1m/s

KE = 1/2 *10*(12-(-1)2) = 0J

no change in kinetic energy

Part-3

Angular momentum = M(rXV)

=10*(1/2*-1)

=-5 Kg m/s^2

Here negative sign implies it is going in to the plane.

Thanks.Hope it helped.

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