(10%) Problem 10: A solid disk of mass M= 9.5 kg and radius R rotates in the z-y
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(10%) Problem 10: A solid disk of mass M= 9.5 kg and radius R rotates in the z-y plane as showin 0.84 m ©theexpertta.com 33% Part (a) 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, o, and t Grade Summary 5% 95% 7 8 9 Attempts remaining: 4 (5% per attempt) detailed view 5% 0 END I give up! Hints: 1 % deduction per hint. Hints remaining: 3 Feedback: 1% deduction per feedback. 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 and R? 33% Part (c) If, as soon as the angular speed is = 5 rad/s, the force is immediately removed and a mass m = 0.35 kg is dropped at r = 0.41 m on the disc and sticks there, what would be the new rotational velocity of the disc in rad/s?Explanation / Answer
M = 9.5 kg
R = 0.84 m
m = 0.35 kg
r = 0.41 m
= 5 rad/s
a) torque = I = ½mr² * /t = MR² / t
b) = MR² / t = F * R, so F = MR/t
c) Conserve momentum: initial L = final L
Io * = If * f
where Io, If are the initial, final moments of inertia and f is the final angular velocity
½MR² = (½MR² + mr²)*f f = MR² / (MR² + 2mr²)
where m and r are the mass and distance from the axis of the added mass.
Plugging in values, I get
f = 4.91 rad/s
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