Q: A car is moving along a flat curve. If the fuzzy dice hanging from the rearview mirror swings at an angle $$\theta$$ from the vertical, what does this angle tell you about the car's speed?

The larger the angle $$\theta$$, the higher the speed $$v$$

Question 1

A car drives around a circular highway curve of radius $$R$$ with constant speed $$v. If $$the car doubles its speed, by what factor must the radius of curvature be increased to maintain the same centripetal acceleration?

Accepted Answer

2

Question 2

Which of the following best describes the direction of centripetal acceleration for an object in uniform circular motion?

Accepted Answer

Toward the center of the circle

Question 3

A car is moving along a flat curve. If the fuzzy dice hanging from the rearview mirror swings at an angle $$	heta$$ from the vertical, what does this angle tell you about the car's speed?

Accepted Answer

The larger the angle $$	heta$$, the higher the speed $$v$$

Question 4

At the top of a vertical circular loop, what is the minimum speed $$v_{min}$$ required for a car of mass $$m to $$stay on the track?

Accepted Answer

$$v_{min} = \sqrt{g r}$$

Question 5

Newton’s Law of Universal Gravitation states that the gravitational force between two point masses $$m_1$$ and $$m_2$$ separated by a distance $$r is$$:

Accepted Answer

$$F = G \frac{m_1$ m_2$}{r^2$}$$

Question 6

An astronaut is standing on a newly discovered planet with the same mass as Earth but twice the radius. How does her weight on this planet compare to her weight on Earth?

Accepted Answer

It is one-fourth her weight on Earth.

Question 7

For a satellite of mass $$m in a $$circular orbit of radius $$r$$ around a planet of mass $$M$$, which equation gives the orbital speed $$v$$?

Accepted Answer

$$v = \sqrt{\frac{GM}{r}}$$

Question 8

Two satellites are to be put into geosynchronous orbits above the Earth, one with mass 500 kg and one with mass 1000 kg. Which will orbit closer to the Earth?

Accepted Answer

Both will orbit at the same distance

Question 9

Which of the following is true about the gravitational force you exert on the Earth compared to the force the Earth exerts on you?

Accepted Answer

You exert an equal force on the Earth as it exerts on you.

Question 10

A battleship simultaneously fires two shells at two abandoned ships, A and B. At the peak of each shell’s trajectory, the radius of curvature of the path is larger for ___ and the radial acceleration is larger for ___.

Accepted Answer

"shell A", "shell A"

Question 11

A battleship simultaneously fires two shells at two abandoned ships, A and B. Which statement best describes the horizontal components of the shells’ velocities?

Accepted Answer

Both shells move with equal horizontal velocity components.

Question 12

Which of the following is a correct expression for the period $$T_{orb} of a $$satellite in a circular orbit of radius $$r$$ around a planet of mass $$M$$?

Accepted Answer

$$T_{orb}^2 = \frac{(2\pi)^2$}{GM} r^3$

Question 13

Near Earth’s surface, the acceleration due to gravity $$g is $$given by which formula?

Accepted Answer

$$g = \frac{GM_E}{R_E^2$}$$

Question 14

If the Earth were not a perfect sphere but had a significant bulge at the equator, which of the following would be true about the gravitational force at the equator compared to the poles?

Accepted Answer

The gravitational force at the equator would be less than at the poles.

Question 15

Which of the following statements about centripetal force is correct?

Accepted Answer

Centripetal force is the net force causing circular motion, always pointing toward the center.

Question 16

A satellite is in a circular orbit around Earth at a constant altitude. If the satellite’s orbital radius is increased, what happens to its orbital speed?

Accepted Answer

It decreases.

Question 17

Which of the following is a simplifying assumption often made when analyzing orbital motion in the solar system?

Accepted Answer

The mass of one object is much greater than the other.

Question 18

For a sphere of uniform density, the gravitational force outside the sphere can be calculated as if all the mass were concentrated at:

Accepted Answer

The center of the sphere

Question 19

Which of the following best explains why the gravitational force between two objects decreases as the distance between them increases?

Accepted Answer

Because gravity is an inverse square law: $$F \propto \frac{1}{r^2$}$$

Gravitation and Circular Motion: Centripetal Acceleration, Newton's Law of Universal Gravitation, and Orbital Motion

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