Q: A table saw blade has a radius of $$0.125\ \mathrm{m}$$ and spins at $$3600\ \mathrm{rpm}. $$What is the acceleration of a tooth at the edge of the blade?

$$a = (2\pi f)^2$ r$$,\ f = 60\ \mathrm{Hz},\ a = (2\pi \times $$60)^2$$ \times 0.125 \approx 1.8 \times $$10^4$$\ \mathrm{$$m/s^2$$}$

Q: A $$70\ \mathrm{m}$$ radius racetrack is banked at $$15^\circ. At $$what speed can a car take the turn without relying on friction?

$$v = \sqrt{r g \tan \theta} = \sqrt{70 \times 9.8 \times \tan 15^\circ} \approx 14\ \mathrm{m/s}$$

Question 1

A car of mass $$1500\ \mathrm{kg} is $$rounding a flat curve of radius $$20\ \mathrm{m} at $$maximum speed without skidding. If the coefficient of static friction between the tires and the road is $$1.0$$, what is the maximum speed the car can have?

Accepted Answer

$$v_{\mathrm{max}} = \sqrt{(1.0)(9.8\ \mathrm{m/s^2$})(20\ \mathrm{m})} \approx 14\ \mathrm{m/s}$$

Question 2

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

Accepted Answer

It is directed toward the center of the circle.

Question 3

A table saw blade has a radius of $$0.125\ \mathrm{m}$$ and spins at $$3600\ \mathrm{rpm}. $$What is the acceleration of a tooth at the edge of the blade?

Accepted Answer

$$a = (2\pi f)^2$ r$$,\ f = 60\ \mathrm{Hz},\ a = (2\pi 	imes $$60)^2$$ 	imes 0.125 \approx 1.8 	imes $$10^4$$\ \mathrm{$$m/s^2$$}$

Question 4

A $$70\ \mathrm{m}$$ radius racetrack is banked at $$15^\circ. At $$what speed can a car take the turn without relying on friction?

Accepted Answer

$$v = \sqrt{r g 	an 	heta} = \sqrt{70 	imes 9.8 	imes 	an 15^\circ} \approx 14\ \mathrm{m/s}$$

Question 5

Which of the following statements about apparent weight on a roller coaster is correct?

Accepted Answer

At the top of a loop, the apparent weight is less than the true weight.

Question 6

A $$60\ \mathrm{kg}$$ astronaut orbits Earth in a spacecraft. What is her weight while in orbit?

Accepted Answer

Zero, because she is in free fall and experiences weightlessness.

Question 7

According to Newton’s law of universal gravitation, what happens to the gravitational force between two masses if the distance between them is doubled?

Accepted Answer

The force decreases by a factor of 4.

Question 8

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

Accepted Answer

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

Question 9

Which of the following is NOT a real force acting on a passenger in a car turning a corner?

Accepted Answer

Centrifugal force

Question 10

A $$70\ \mathrm{kg}$$ person stands on three different planets: A ($$M_A = 3M_{\mathrm{Earth}},\ R_A = R_{\mathrm{Earth}}$$), B ($$M_B = M_{\mathrm{Earth}},\ R_B = 2R_{\mathrm{Earth}}$$), and C ($$M_C = 0.5M_{\mathrm{Earth}},\ R_C = 0.5R_{\mathrm{Earth}}). On $$which planet is her weight greatest?

Accepted Answer

Planet C

Question 11

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

Accepted Answer

It will move in a straight line tangent to the circle at the point where friction disappeared.

Question 12

The period $$T of a $$satellite in a circular orbit of radius $$r$$ around a planet of mass $$M is $$given by:

Accepted Answer

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

Question 13

Which of the following best explains why astronauts experience weightlessness while orbiting Earth?

Accepted Answer

They are in continuous free fall around Earth.

Question 14

A $$2\ \mathrm{kg}$$ object moves in a circle of radius $$0.5\ \mathrm{m} at a $$constant speed of $$4\ \mathrm{m/s}. $$What is the magnitude of the net force acting on it?

Accepted Answer

$$F = m a = m \frac{v^2$}{r} = 2 	imes \frac{16}{0.5} = 64\ \mathrm{N}$$

Question 15

If the frequency of rotation of a wheel doubles, what happens to the centripetal acceleration of a point on its rim?

Accepted Answer

It quadruples.

Question 16

Which of the following is true about the velocity vector of an object in uniform circular motion?

Accepted Answer

It is always perpendicular to the acceleration vector.

Question 17

A planet has twice the mass and twice the radius of Earth. What is the acceleration due to gravity on its surface?

Accepted Answer

$$g = \frac{G M}{R^2$} = \frac{G 	imes 2M_{\mathrm{Earth}}}{(2R_{\mathrm{Earth}})^2$} = \frac{2G M_{\mathrm{Earth}}}{4R_{\mathrm{Earth}}^2} = \frac{1}{2}g_{\mathrm{Earth}}$$

Question 18

Which of the following is a correct statement about Newton’s law of gravity?

Accepted Answer

The gravitational force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

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

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