Name:______________________________Class:__________________ Date:__________________
Circular Motion and Gravitation
Section Study Guide
Teacher Notes and Answers
MOTION IN SPACE
CIRCULAR MOTION
1. a. According to Copernicus, Earth and the
other planets each move in a perfect circle
around the sun.
b. According to Kepler’s First Law, Earth
and the other planets each move in an
elliptical orbit with the sun at one focus.
2. t1 = t2
3. T2 r3
4. Newton derived Kepler’s laws from the
universal law of gravitation.
5. T = 3.17 107 s; vt = 2.98 104 m/s
1. a. yes
b. The car has a non-zero acceleration
because the direction of motion is changing.
c. The direction of centripetal acceleration is
toward the center of the circle. In this case,
the direction is toward the center of the
Ferris wheel.
d. 4.8 10 2 m/s2
2. a. the wire
b. centripetal force
c. The centripetal force acts toward the
center of the circular motion.
d. inertia
e. 32.0 m/s
TORQUE AND SIMPLE MECHANICS
1. a. Fd, Fe, Ff, Fg
b. Fe exerts the largest torque because it has
the largest lever arm.
2. a. 1.2 104 J
b. 120 N
c. 110 m
d. greater
3. a. 0.92
b. 0.90
c. 0.94
NEWTON’S LAW OF UNIVERSAL
GRAVITATION
1. a. 2
b. 4
c.
d. 1
2. a. double one mass, double the force
b. double both masses, quadruple the force
c. double the radius, decrease the force to
d. If measured in the opposite direction, the
force will be in the opposite direction.
3. Because of inertia, objects tend to go in a
straight line. A force is needed to change the
direction of travel.
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Study Guide
Name:______________________________Class:__________________ Date:__________________
Circular Motion and Gravitation
Concept Review
Circular Motion
1. A Ferris wheel car is moving in a circular path at a constant speed.
a. Is the car accelerating?_____________________________________________
b. How can the car have a non-zero acceleration if the speed is constant?
_________________________________________________________________
_________________________________________________________________
c. What is the direction of centripetal acceleration?
_________________________________________________________________
d. What is the magnitude of the centripetal acceleration if the tangential speed of
the car is 2.0 m/s and the radius of the wheel is 83 m?
_________________________________________________________________
2. The hammer throw is a track-and-field event in which the thrower swings a heavy
metal ball (the “hammer”) on a wire in a circular motion, then releases the wire,
sending the hammer flying.
a. What provides the force to keep the hammer moving in a circle before the wire
is released?
_________________________________________________________________
b. What is the name for this force? _____________________________________
c. In what direction does this force act? _________________________________
_________________________________________________________________
d. What is the term for the hammer’s tendency to move in a straight line?
_________________________________________________________________
e. Suppose the hammer has a mass of 7.26 kg, the wire is 1.00 m long, and the
force keeping the hammer moving in a circle is 7.43 103 N. What will the
hammer’s speed be when the thrower releases the wire?
Original content Copyright © by Holt, Rinehart and Winston. Additions and changes to the original content are the responsibility of the instructor.
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Study Guide
Name:______________________________Class:__________________ Date:__________________
Circular Motion and Gravitation
Concept Review
Newton’s Law of Universal Gravitation
m1m2
. Consider a system
r2
of two masses, m1 = m2 = M, at a distance r = Ro. The gravitational force on each
MM
M2
= G 2 . Find the ratio of the new
of these masses would be Fo = G
2
Ro
Ro
gravitational force to the original force, Fo , for each of the following situations.
1. Newton’s universal law of gravitation states that Fg = G
a. m1 = M, m2 = 2M, r = Ro. ___________________________________________
b. m1 = m2 = 2M, r = Ro. _____________________________________________
c. m1 = m2 = M, r = 2Ro. _____________________________________________
d. m1 = m2 = M, r = Ro. _____________________________________________
2. For each situation in item 1, write a sentence that summarizes in words what has
changed and how that change has affected the gravitational force.
a. _______________________________________________________________
_________________________________________________________________
b. _______________________________________________________________
_________________________________________________________________
c. _______________________________________________________________
_________________________________________________________________
d. _______________________________________________________________
_________________________________________________________________
3. Why is a force necessary to create circular motion?
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
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Study Guide
Name:______________________________Class:__________________ Date:__________________
Circular Motion and Gravitation
Concept Review
Motion in Space
1. Claudius Ptolemy proposed that planets travel in small circles, called epicycles,
while they simultaneously travel in larger circles around Earth.
a. According to Nicolaus Copernicus, how do Earth and the other planets move?
_________________________________________________________________
_________________________________________________________________
b. According to Kepler’s first law, how do Earth and the other planets move?
_________________________________________________________________
_________________________________________________________________
2. Examine the diagram above. If the area A1 equals the area A2, what can you
conclude about the relationship between t1 and t2?
_________________________________________________________________
3. Kepler’s third law describes the relationship between a planet’s orbital period, T,
and the mean distance between the planet and the sun, r. Express this relationship
as a proportion, in symbolic form.
_________________________________________________________________
4. How did Newton use Kepler’s laws to support his theory of gravitation?
_________________________________________________________________
_________________________________________________________________
5. Earth travels around the sun in a nearly circular orbit at a mean distance of 1.50 1011 m. The sun’s mass is 1.99 1030 kg. Calculate Earth’s orbital period and
orbital speed.
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Name:______________________________Class:__________________ Date:__________________
Circular Motion and Gravitation
Concept Review
Torque and Simple Mechanics
1. Use the diagram at right to complete the following items. The arrows represent
force vectors, and the dashed lines
represent the lines of action of the
forces.
a. Identify the forces that exert a torque
on the object.
______________________________
b. If each force has the same magnitude,
which force exerts the largest torque?
Explain your answer.
______________________________
______________________________
______________________________
______________________________
2. A pulley system with a mechanical advantage of 15 is used to lift a 1750 N piano
to a third-floor balcony that is 7.0 m above the ground.
a. If friction is negligible, how much work must be done? __________________
b. What applied force must the movers use? _____________________________
c. How much rope will the movers pull in? ______________________________
d. If friction is not negligible, is the input energy greater than or less than your
answer to part a?
_________________________________________________________________
3. Calculate the efficiency of the following.
a. Win = 1850 J, Wout = 1700 J _________________________________________
b. an object weighing 150 N is lifted 9.0 m using 1500 J of energy ____________
c. a force of 150 N is exerted along a 3.0 m inclined plane to raise an object
weighing 425 N to a height of 1.0 m _________________________________
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