Question 8 A thin uniform rod has a length of 0.550 m and is rotating in a circl

Question

Question 8 A thin uniform rod has a length of 0.550 m and is rotating in a circle on a frictionless table. The axis of rotation is perpendicular to the length of the rod at one end and is stationary. The rod has an angular velocity of 0.36 rad/s and a moment of inertia about the axis of 2.60x10-3 kg m2 A bug initially standing on the rod at the axis of rotation decides to crawl out to the other end of the rod When the bug has reached the end of the rod and sits there, its tangential speed is 0.100 m/s. The bug can be treated as a point mass. Part A What is the mass of the rod? Express your answer with the appropriate units mrod 2.58x10-2 kg Submit My Answers Give Up Correct Part B What is the mass of the bug? Express your answer with the appropriate units. mbug Value Units Submit My Answers Give Up

Explanation / Answer

Moment of inertia about axis = m L^2 / 3

2.60 x 10^-3 = m x 0.550^2 / 3

m = 0.0258 kg

B) initial angular momentum of system, (bug has zero angular momentum)

pi = Iw = (2.60 x 10^-3 ) (0.36) = 9.36 x 10^-4 kg m^2 / s

finally :

angular moment of bug = m v r = (m x 0.1 x 0.55) = 0.055m

w = v/r = 0.1/0.55 = 0.1818 rad/s

of rod = I w = (2.60 x 10^-3 ) (0.1818) = 4.727 x 10^-4 kg m^2 /s

Using angular momentum conservation,

9.36 x 10^-4 = 0.055m + (4.727 x 10^-4)

m = 8.423 x 10^-3 kg   Or 8.423 g

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