Q: A car of mass $$m is $$turning a corner of radius $$r at a $$constant speed $$v on a $$flat, unbanked road. What is the maximum speed the car can have without sliding, if the coefficient of static friction between the tires and the road is $$\mu_s$$?

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

Q: A 65-kg student sits 0.60 m away from another 65-kg student. What is the magnitude of the gravitational force between them? ($$G = 6.67 \times 10$$^{-11}$$ \ \text{N} \cdot \text{m}^2/\text{kg}^2)$$

$$1.2 \times 10$$^{-7}$$ \ \text{N}$$

Q: A table saw blade has a radius of $$0.125 m $$and spins at $$3600$$ rpm. What is the linear speed $$v of a $$tooth at the edge of the blade?

$$v = 2 \pi r f = 2 \pi (0.125) (60) \approx 47.1 \ \text{m/s}$$

Question 1

A car of mass $$m is $$turning a corner of radius $$r at a $$constant speed $$v on a $$flat, unbanked road. What is the maximum speed the car can have without sliding, if the coefficient of static friction between the tires and the road is $$\mu_s$$?

Accepted Answer

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

Question 2

A 70-kg astronaut is orbiting Earth in the International Space Station. Why does the astronaut feel weightless?

Accepted Answer

Because the astronaut and the station are both in free fall around Earth.

Question 3

A roller coaster car of mass $$m$$ moves with speed $$v at $$the top of a vertical loop of radius $$r. $$What is the minimum speed $$v_c$$ required for the car to stay on the track at the top of the loop?

Accepted Answer

$$v_c = \sqrt{g r}$$

Question 4

Two asteroids attract each other with a gravitational force $$F. If $$the distance between them is doubled, what is the new force?

Accepted Answer

$$\frac{F}{4}$$

Question 5

A coin sits on a turntable rotating at constant speed. What force provides the centripetal acceleration keeping the coin moving in a circle?

Accepted Answer

Static friction

Question 6

A satellite of mass $$m$$ orbits a planet of mass $$M at $$radius $$r. $$What is the speed $$v$$ required for a stable circular orbit?

Accepted Answer

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

Question 7

A car of mass $$m$$ goes through a dip in the road at speed $$v ($$the dip is a circular arc of radius $$r). $$What is the normal force $$n$$ exerted by the road on the car at the bottom of the dip?

Accepted Answer

$$n = m g + \frac{m v^2$}{r}$$

Question 8

A communications satellite is in a geostationary orbit above the equator. What is the period $$T of $$its orbit?

Accepted Answer

$$T = 24$$ hours

Question 9

Which of the following statements about centrifugal force is correct?

Accepted Answer

It is not a real force and does not appear in a free-body diagram.

Question 10

A ball of mass $$m is $$attached to a string and swung in a horizontal circle of radius $$r at $$constant speed $$v. $$What is the tension $$T in $$the string?

Accepted Answer

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

Question 11

A planet has twice the mass and twice the radius of Earth. What is the acceleration due to gravity $$g' at $$its surface compared to Earth's $$g$$?

Accepted Answer

$$g' = \frac{g}{2}$$

Question 12

A 65-kg student sits 0.60 m away from another 65-kg student. What is the magnitude of the gravitational force between them? ($$G = 6.67 	imes 10$$^{-11}$$ \ 	ext{N} \cdot 	ext{m}^2/	ext{kg}^2)$$

Accepted Answer

$$1.2 	imes 10$$^{-7}$$ \ 	ext{N}$$

Question 13

A coin is rotating on a turntable without sliding. If the frictional force suddenly disappears, what path does the coin follow?

Accepted Answer

It moves in a straight line tangent to the circle at that instant.

Question 14

A satellite orbits Earth at radius $$r$$ with speed $$v. If $$the satellite is moved to a higher orbit of radius $$2r$$, what happens to its speed?

Accepted Answer

It decreases by a factor of $$\sqrt{2}.$$

Question 15

A table saw blade has a radius of $$0.125 m $$and spins at $$3600$$ rpm. What is the linear speed $$v of a $$tooth at the edge of the blade?

Accepted Answer

$$v = 2 \pi r f = 2 \pi (0.125) (60) \approx 47.1 \ 	ext{m/s}$$

Question 16

A car is turning a corner on a frictionless, banked road at the ideal speed. What force provides the required centripetal acceleration?

Accepted Answer

The horizontal component of the normal force

Question 17

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

Accepted Answer

Toward the center of the circle

Question 18

A satellite orbits a planet of mass $$M at $$radius $$r. $$What is the period $$T of $$its orbit?

Accepted Answer

$$T = 2 \pi \sqrt{\frac{r^3$}{G M}}$$

Question 19

A 60-kg person stands on three different planets. On which planet is her weight the greatest?

Accepted Answer

The planet with the largest $$\frac{M}{R^2$}$$, where $$M is $$mass and $$R is $$radius.

Chapter 6: Circular Motion, Orbits, and Gravity – Study Notes

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