Q: A 70-kg astronaut is wearing a 30-kg spacesuit. If the acceleration due to gravity on the Moon is $$1.62\ \mathrm{m/s^2$}$$, what is the astronaut's weight on the Moon?

$$100\ \mathrm{kg} \times 1.62\ \mathrm{m/s^2$} = 162\ \mathrm{N}$$

Question 1

A satellite is in a circular orbit of radius $$r$$ around a planet of mass $$M. $$What is the correct expression for the speed $$v$$ required to maintain this orbit?

Accepted Answer

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

Question 2

If the distance between two masses is doubled, by what factor does the gravitational force between them change according to Newton's law of gravity?

Accepted Answer

It decreases by a factor of 4

Question 3

A 70-kg astronaut is wearing a 30-kg spacesuit. If the acceleration due to gravity on the Moon is $$1.62\ \mathrm{m/s^2$}$$, what is the astronaut's weight on the Moon?

Accepted Answer

$$100\ \mathrm{kg} 	imes 1.62\ \mathrm{m/s^2$} = 162\ \mathrm{N}$$

Question 4

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 5

A fan blade is slowing down. What are the signs of its angular velocity $$\omega$$ and angular acceleration $$\alpha$$?

Accepted Answer

$$\omega is $$positive and $$\alpha is $$negative

Question 6

A crankshaft in a car engine is turning at 3000 rpm. What is its angular speed in radians per second?

Accepted Answer

$$314\ \mathrm{rad/s}$$

Question 7

Which of the following is the correct relationship between linear speed $$v$$ and angular speed $$\omega$$ for a point at a distance $$r$$ from the axis of rotation?

Accepted Answer

$$v = \omega r$$

Question 8

A force $$F is $$applied perpendicular to a door at a distance $$r$$ from the hinge. What is the torque $$	au$$ produced by this force?

Accepted Answer

$$	au = rF$$

Question 9

A geostationary satellite orbits the Earth with a period of 24 hours. If the mass of the Earth is $$5.98 	imes 10$$^{24}$$\ \mathrm{kg}$$ and $$G = 6.67 	imes 10$$^{-11}$$\ \mathrm{N\cdot m^2$/kg^2$$}$$, which equation would you use to solve for the radius r$ of its orbit?

Accepted Answer

$$T^2$$ = \dfrac{4\$$pi^2$$ $$r^3$$}{GM}$$

Question 10

Which of the following statements about apparent weight in circular motion is correct?

Accepted Answer

Apparent weight is the normal force exerted by a surface and can differ from true weight.

Question 11

Two satellites have circular orbits with the same radius around Earth, but different masses. Which has a higher speed?

Accepted Answer

They have the same speed

Question 12

What is the angular displacement $$\Delta 	heta in $$radians for a particle that completes 3 full revolutions?

Accepted Answer

$$6\pi$$ radians

Question 13

A force of $$1500\ \mathrm{N} is $$applied to a capstan at a distance $$R$$ from the axis. A sailor pushes at a distance $$7R in $$the opposite direction. What force $$F$$ must the sailor apply to keep the capstan turning at constant speed?

Accepted Answer

$$F = \dfrac{1500\ \mathrm{N}}{7}$$

Question 14

Which of the following is the correct expression for the gravitational force between two masses $$m_1$$ and $$m_2$$ separated by a distance $$r$$?

Accepted Answer

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

Question 15

A particle moves in a circle of radius $$r at $$constant speed $$v. $$What is the magnitude of its centripetal acceleration?

Accepted Answer

$$a = \dfrac{v^2$}{r}$$

Question 16

Which of the following is true about the torque produced by a force applied at an angle $$\phi to $$the radial line at a distance $$r$$ from the pivot?

Accepted Answer

$$	au = rF\sin\phi$$

Question 17

Which of the following is the correct unit for torque?

Accepted Answer

Newton-meter (N-m)

Question 18

If a rotating rigid body has an angular acceleration $$\alpha$$ and a moment of inertia $$I$$, what is the net torque $$	au_{net}$$ acting on it?

Accepted Answer

$$	au_{net} = I\alpha$$

Physics for Life Sciences I: Circular Motion, Gravity, and Rotational Motion (Lecture 11 Study Notes)

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