A solid disk of mass M-1.5 kg and radius R = 0.89 m rotates in the z-y plane as

Question

A solid disk of mass M-1.5 kg and radius R = 0.89 m rotates in the z-y plane as shown. Randomized Variables Write an expression for the magnitude of the net torque required for the disc to achieve a given rotational speed when starting from rest in terms of M, R, w, and t H ^ 33% 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 z and /??H ^ 33% Part (c) If, as soon as the angular speed is o)-32 rad/s, the force is immediately removed and a mass m -13 kg is dropped at r = 0.49 m on the disc and sticks there, what would be the new rotational velocity of the disc in rad/s?

Explanation / Answer

a) we know, moment of inertia of wheel, I = 0.5*M*R^2

angular acceleration, alfa = w/t

we know, Totque, T = I*alfa

= 0.5*M*R^2*w/t

= M*R^2*w/(2*t)

b) we now, T = R*F*sin(90)

==> F = T/R

= M*R*w/(2*t)

c) Apply conservation of momentum

(0.5*M*R^2)*wi = (0.5*M*R^2 + m*r^2)*wf

wf = (0.5*M*R^2)*wi/(0.5*M*R^2 + m*r^2)

= (0.5*1.5*0.89^2)*32/(0.5*1.5*0.89^2 + 1.3*0.49^2)

= 20.98 rad/s

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