A disk of radius R and mass M = 10 g is rotating freely about a fixed axis throu

Question

A disk of radius R and mass M = 10 g is rotating freely about a fixed axis through its center with angular velocity w = 11 rad/s. A spider of mass m = 0.5 g descends onto the disk and goes along for the ride. The moment of inertia of the disk is I = (1/2)MR2.

(a) Which principle will allow you to calculate the angular velocity after the spider has landed?

(b) Calculate the angular velocity after the spider has landed on the disk.

(c) If the spider starts crawling towards the center of the disk, the angular velocity is going to:
[1] increase, [2] decrease, or [3] remain the same. Give a short explanation for your answer.

Explanation / Answer

M = 0.01kg, =11rad/s, m=0.0005kg, I = 0.5*M*R^2

(a) conservation of angular momentum

(b) I11 = I22

0.5*M*R^2*1 = (0.5*M*R^2+m*R^2)2

0.5*0.01*11 = (0.5*0.01 + 0.0005)2

2 = 10rad/s

(c) When the spider starts moving towards the centre, the Moment of inertia of spider = mr^2 decreases and to compensate the decrease in moment of inertia, angular speed increases.

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