Problem 1 : A solid disk of mass M = 5 kg and radius R = 0.88 m rotates in the z

Question

Problem 1: A solid disk of mass M = 5 kg and radius R = 0.88 m rotates in the z-y plane as shown.

Randomized VariablesM = 5 kg
R = 0.88 m
Part (a) Write an expression for the magnitude of the net torque required so that the disc achieves a rotational velocity ? = 23 rad/s in t = 1.3 seconds when starting from rest in terms of M, R, ?, and t. (?0 = 0)


Part (b) What is an expression for the force that produces this torque if it is applied to the edge of the disc and in a direction that is tangent to the disc in terms of ? and R?


Part (c) If when ? is achieved by the disc the force is immediately removed and a mass m = 0.9 kg is dropped at r = 0.33 m on the disc and sticks there, what would be the new rotational velocity of the disc in rad/s? A solid disk of mass M = 5 kg and radius R = 0.88 m rotates in the z-y plane as shown. Write an expression for the magnitude of the net torque required so that the disc achieves a rotational velocity ? = 23 rad/s in t = 1.3 seconds when starting from rest in terms of M, R, ?, and t. (?0 = 0) What is an expression for the force that produces this torque if it is applied to the edge of the disc and in a direction that is tangent to the disc in terms of ? and R? If when ? is achieved by the disc the force is immediately removed and a mass m = 0.9 kg is dropped at r = 0.33 m on the disc and sticks there, what would be the new rotational velocity of the disc in rad/s?

Explanation / Answer

torque T = Iw^2

where I is moment of inertia

and w is angular velocity

I of disk is 1/2MR^2

I=1.936

T=1.936*23*23

=1024.14

torque is also given by

T=R*F

F=T/R

=1163.8

c)

when a mass is placed on the disk

then the new moment of inertia is

I'=1/2MR^2+md^2

=1.936+.098

=2.03

now conserving initial and final angular angular momentum

Iw=I'w'

w'=Iw/I'

   =1.936*23/2.03

   =21.93 rad/s

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