Question

QUESTION 1:

A thin uniform rod has a length of 0.400 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 0.35 rad/s and a moment of inertia about the axis of 2.90×10⁻³ 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 0.113 m/s . The bug can be treated as a point mass.

A) What is the mass of the rod?

B) What is the mass of the bug?

QUESTION 2:

A hollow, spherical shell with mass 1.60 kg rolls without slipping down a slope angled at 35.0 degree.

A) Find the acceleration. Take the free fall acceleration to be g= 9.80 m/s2

B) Find the friction force.Take the free fall acceleration to be g= 9.80 m/s2

C) Find the minimum coefficient of friction needed to prevent slipping.

Answer 1

PROBLEM 1:

PART A:

The moment of inertia of a rod about its one end is given by

So, the mass of the rod is 54.375 g.

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PART B:

The initial angular momentum of the system is

When the bug is at the other end, the moment of inertia of the system is

The final angular velocity can be calculated by

So, the final angular momentum is

Conservation of angular moment gives us

So, the mass of the bug is 4.33 g.

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