Q: A ball moves in a circle of radius 10 m and completes 100 rotations in 60 seconds. What is its speed $$v$$?

$$v = \frac{2\pi \times 10 \times 100}{60} m/s$$

Q: A space station of diameter 500 m is spun about its axis to simulate gravity. What RPM must it turn so the astronauts inside feel an acceleration equal to $$g$$?

$$\text{RPM} = \sqrt{\frac{g}{4\pi^2$ R}} \times 60$$

Question 1

A windmill blade completes 20 revolutions per minute (RPM). What is the period $$T of $$one revolution in seconds?

Accepted Answer

$$T = 3 s$$

Question 2

A ball moves in a circle of radius 10 m and completes 100 rotations in 60 seconds. What is its speed $$v$$?

Accepted Answer

$$v = \frac{2\pi 	imes 10 	imes 100}{60} m/s$$

Question 3

A space station of diameter 500 m is spun about its axis to simulate gravity. What RPM must it turn so the astronauts inside feel an acceleration equal to $$g$$?

Accepted Answer

$$	ext{RPM} = \sqrt{\frac{g}{4\pi^2$ R}} 	imes 60$$

Question 4

A 3 kg block is tied to a 2 m string and slides around a frictionless table in a circle, completing a rotation every 4 seconds. What is the tension in the string?

Accepted Answer

$$T = m \frac{v^2$}{r}$$, where $$v = \frac{2\pi r}{T}$$

Question 5

A 0.5 kg ball is tied to a 4 m cord and spins in a horizontal plane at constant speed, with the cord making a $$30^\circ$$ angle with the vertical. What is the correct approach to determine the ball's speed?

Accepted Answer

Resolve forces in both vertical and horizontal directions, set $$T \cos 	heta = m g$$ and $$T \sin 	heta = m v^2$ / r$$

Question 6

What force keeps a car in circular motion as it travels around a flat curve?

Accepted Answer

Centripetal force provided by friction

Question 7

An 800 kg car drives around a flat curve of radius 50 m. If the coefficient of static friction is 0.5, what is the maximum speed before slipping?

Accepted Answer

$$v_{max} = \sqrt{\mu_s g r}$$

Question 8

For a banked curve with no friction, what is the equation for the speed at which a car can travel without slipping?

Accepted Answer

$$v = \sqrt{g r 	an 	heta}$$

Question 9

A bobsled moves in a circle of radius 10 m at a speed of 4 m/s. What is its centripetal acceleration?

Accepted Answer

$$a_c = \frac{v^2$}{r} = \frac{16}{10} = 1.6 m/s$^2$$

Question 10

You are sitting in a rollercoaster at the bottom of a loop of radius 10 m, moving at 30 m/s. What is the centripetal acceleration?

Accepted Answer

$$a_c = \frac{v^2$}{r} = \frac{900}{10} = 90 m/s$^2$$

Question 11

A car of mass 1200 kg moves over the top of a bump at a constant speed of 9 m/s. The radius of curvature is 20 m. What is the normal force exerted by the road?

Accepted Answer

$$N = m g - m \frac{v^2$}{r}$$

Question 12

A satellite orbits Earth in a circular orbit. What force keeps it in orbit?

Accepted Answer

Centripetal force provided by gravity

Question 13

The orbital speed $$v of a $$satellite in circular orbit of radius $$r$$ around a planet of mass $$M is $$given by:

Accepted Answer

$$v = \sqrt{\frac{G M}{r}}$$

Question 14

If the launch velocity of a probe around a planet is less than the minimum orbital speed, what will happen?

Accepted Answer

It will crash into the planet

Question 15

Two satellites orbit a planet of diameter $$8 	imes 10^7$ m. Satellite A has mass 68 kg, orbital radius 6$$ 	imes $$10^7 m$$, and speed 3000 m/s. Satellite B has mass 84 kg, orbital radius $$9 	imes 10^7$ m. What is the orbital speed of satellite B?

Accepted Answer

$$v_B = \sqrt{\frac{G M}{r_B}}$$

Question 16

A baseball is thrown horizontally on the surface of a spherical asteroid of mass $$7 	imes 10$$^{14}$$ kg and diameter 22 km. What is the minimum speed to just barely go around the asteroid?

Accepted Answer

$$v = \sqrt{\frac{G M}{r}}$$

Question 17

Which of the following statements about centripetal force is correct?

Accepted Answer

It always points toward the center of the circle

Question 18

For circular motion in the vertical plane, how does the speed of the object change as it moves from the bottom to the top of the loop?

Accepted Answer

Speed decreases due to gravity

Circular Motion and Satellite Orbits: Study Guide

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