Question

2. Which has more rotational inertia: A solid, uniform sphere of mass 100kg, or a mostly hollow spherical shell of mass 100kg?

a.They both have the same rotational inertia

b.Solid Sphere

c.Hollow Sphere

3.If a bicycle starts from rest and is pedaled normally until the bike is moving at 6 meters per second across level ground, what kinds of energy have its tires been given? (Select all that apply)

a.Rotational Kinetic Energy

b.Translational Kinetic Energy

c.Gravitational Potential Energy

d.Elastic Potential Energy

4.A small car is driving around a circular track repeatedly at a constant speed of 30 meters per second. If the track measures 120 meters all the way around, the frequency is how many Hertz?(1 Hertz = 1 cycle per second)

5.A student standing on a freely spinnable platform is at rest and holding up a counterclockwise spinning gyroscope as in the picture. If the student suddenly flips the gyroscope upside down, what will happen to them on the platform.

a.The student will feel a force that will cause them to lean over to the left.

b.The student will begin to spin clockwise.

c.The student will feel a force that will cause them to lean over to the right.

d.The student will begin to spin counterclockwise.

Answer 1

Solution

2. c. Hollow sphere (assuming that both of them have same radius)

The moment of inertia of solid sphere (about axis through its center) is given by,

Whereas that of a spherical shell is,

Thus here given that both shell and sphere have same masses. Thus we need radius of them R too in order to calculate M.I. Assuming both if them have same radius we can see,

3. a. Rotational kinetic energy and b. Translational kinetic energy.

Since the tires are both rotating about their axis and also having a translational motion, they possess both rotational and translational kinetic energy. Also since it is a level ground no height difference occures hence no gravitational potential.

4. 0.25 Hz

Given the circumference of circular path 120m and speed of car 30 m/s. Thus frequecy of circular motion,

5. d. The student begin to spin counter clockwise.

This is due to the conservation of angular momentum. Since the combined system of platform student and gyroscope is in equilibrium and having a constant a net angular momentum in the counter clockwise (due to spinning gryo) initially. Thus when student flips the gyro it changes to clockwise spinning but there are no external torques on the combined system. It was all an internal process. Thus the conservation of angular momentum will be valid and for that the entire platform have to spin counter clockwise direction which will make the total angular momentum still in the counter clockwise manner and conserving it.