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Circular Motion Review
1.) A car travels around a curved path that has a radius of 225m at a constant speed of
26.0 m/s. When is the centripetal acceleration of the car? [3.00m/s2, towards
center]
2.) A particle with a mass of 4.2x10-3kg is travelling in a circle with a radius of 2.0x10-3m
with a speed of 8.0m/s.
a. Calculate the period? [1.6x10-3s]
b. What is the centripetal acceleration? [3.2x104 m/s2, towards center]
c. What is the magnitude of the force acting on it? [1.3x102 N]
3.) A kid measures a time of 11.0s for a toy race car to go around a horizontal circular
loop 5 times. If the diameter of the circular loop is 75.0cm, what is the speed of the
race car? [1.07 m/s]
4.) An electron (m=9.11x10-31kg) moves in a circular motion with a radius of 2.00x10-2m.
If the force acting on the electron is 4.60x10-14N, what is the speed of the electron?
[3.18x107 m/s]
5.) How fast can a 1.6x103 kg car safely travel around a curve on a horizontal road if the
coefficient of friction between the car and the road is 0.60? The radius of curvature is
55m. [18 m/s]
6.) A 0.150 kg mass is twirled in a horizontal circle with a radius of 0.75m at a rate of
150 rpm at the end of a string. What is the magnitude of tension in the string?
[27.8N]
7.) A 1.2kg ball is attached to a thin rod and swung in a vertical circle of radius 1.5m with
a constant speed of 4.0m/s. What is the force in the rod at the high and low points?
[Fapp, high = 1.0N & Fapp, low = 25N]
8.) You and your bike have a total mass of 95.0kg and you are riding your bike over a
rise of a hill that has a radius of 10.0m. How fast must you be travelling so that your
bike just loses contact with the path? [9.90 m/s]
9.) A student, who has a mass of 50.0kg, is riding through a dip (radius of curvature is
15.0m) on a roller coaster at a speed of 10.0m/s. What is the force normal exerted
on the student (ie. this is also the student’s apparent weight) at the bottom of the dip?
[824 N]
10.) A 1.75 kg mass is tied to the end of a string and is swung in a vertical circle with a
radius of 1.10m. The string will break if it is subjected to a force greater than 262N.
What is the maximum speed that this mass can travel in a vertical circle so the string
does not break? [12.4 m/s]
11.) Two bodies have masses of 3.0x105kg and 6.7x107kg and their centers are
separated by a distance of 4.0x103m. What is the magnitude of the
attractive/gravitational force acting on each other? [8.4x10-5 N]
12.) The force of gravity between two masses is 3.55x10-4N. If both masses are
increased by a factor of 2 and the separation between the masses is tripled, what is
the new gravitational force acting on the masses? [1.58x10-4 N]
13.) If an object has a weight of 9.75x102N on the surface of the earth, what is its weight
at a distance of 8.60x105m above the earth’s surface? [757 N]
14.) Three masses, A, B, and C have respective masses of 4.0kg, 2.0kg, and 5.0kg. The
masses are located on a 5.0cm straight line with A and C at opposite ends. Mass B
is 2.0cm from mass A, as shown in the diagram. What is the net gravitational force
on B due to the presence of the other two masses? [5.9x10-7 N, left]
5.0 cm
A
B
C
2.0 cm
15.) Calculate the acceleration due to gravity 1500km from the surface of the earth.
[6.43 m/s2]
16.) A mass on the surface of the earth has a weight of 39.2N. If the same mass is taken
to the surface of Mars and has a weight of 28.4N, what is the gravitational field
strength near the surface of Mars? [7.11 N/kg]
17.) Mass A is 150kg and mass B is 290kg. Use the following diagram to calculate the
net gravitational field at point P. [3.23x10-7 N/kg, 17.2o E of N]
A
18.0
3 cm
cm
P
B

45.0 cm
18.) On the surface of an unknown planet, which has a mass of 1.33x1025 kg, an object
has a weight of 260 N and a mass of 95.0 kg. What is the radius of this planet?
[1.80x107 m]
19.) An object with a mass of 325kg is falling towards to earth’s surface at a rate of
6.45m/s2 due to the earth’s gravitational force. At what distance from the earth
surface is the object when it is falling at a rate of 6.45m/s2? [1.49x106 m]
20.) How far from the surface of the earth is the gravitational field strength 1.22 N/kg?
[1.17x107 m]
21.) The gravitational field strength at a point in space is 3.46N/kg. What is the weight of
an object at this point if it has a mass of 8.50x102kg? [2.94x103 N]
22.) An object has a weight of 9.60x102N when it is 2600km above the surface of the
earth. What is the mass of the object? [194 kg]
23.) In what position of its orbit does a planet move to slowest? [Kepler’s Law states
when its radius is the largest, the planet moves the slowest]
24.) A 625kg satellite is orbiting a planet at with an orbital radius of 3.43x106m. If the
mass of the planet is 3.18x1023 kg, what is the orbital speed of the satellite?
[2.49x103 m/s]
25.) A piece of space junk has an orbital radius of 6.84x105m around an unknown mass.
If the space junk can make 7 complete orbits in 24.0 hours, what is the mass of the
unknown mass? [1.24x1021 kg]
26.) An artificial satellite with a mass of 572kg is put into a circular orbit about the earth.
If the satellite is 5.63x103km above the surface of the earth, how long (in hours) will it
take the satellite to make one full revolution around the earth? [3.64 hours]
27.) An asteroid is orbiting around Jupiter with a speed of 3.12x104m/s. If the mass and
radius of Jupiter, respectively, are1.90x1027 kg and 6.99x107 m, how far above
Jupiter’s surface is the asteroid? [6.03x107 m]