Question

The assembly shown in the figure below consists of a thin rod of length

ℓ = 23.2 cm

and mass

* m* = 1.20 kg

with a solid sphere of diameter

* d* = 10.0 cm

and mass

* M* = 2.00 kg

attached to its top. The assembly is free to pivot about a frictionless axle through the bottom of the rod. The assembly is initially vertical and at rest when it starts to rotate clockwise.

A thin rod of length ℓ and mass *m* is upright with a
sphere of diameter *d*and mass *M* attached to the
rod at the bottom of the sphere. A pivot is at the bottom of the
rod and the rod-sphere system rotates in a clockwise direction.

(a)

After the combination rotates through 90 degrees, what is its rotational kinetic energy (in J)?

J

(b)

What is the angular speed (in rad/s) of the rod and sphere?

rad/s

(c)

What is the linear speed (in m/s) of the center of mass of the sphere?

m/s

(d)

How does it compare with the speed had the sphere fallen freely through the same distance of 28.2 cm? (Express your answer as a percentage.)

*v*_{swing} is ---Select--- greater
than less than *v*_{fall} by %.

Answer #1

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