Physics Problems – Applications of Circular Motion
Name ______________________________
Pg 252 Section Review
1. Convert the following angles in degrees, to radians.
a) 25º
b) 35º
c) 128º
d) 270º
2. A mosquito lands on a phonograph record 5.0 cm from the record’s center. If the record turns clockwise
so that the mosquito travels along an arc length of 5.0 cm, what is the mosquito’s angular displacement?
3. A bicyclist rides along a circular track. If the bicyclist travels around exactly half the track in 10.0 s,
what is his average angular speed?
4. Find the angular acceleration of a spinning amusement-park ride that initially travels at 0.50 rad/s then
accelerates to 0.60 rad/s during a 0.50 s time interval.
5. What is the instantaneous angular speed of a spinning amusement-park ride that accelerates from 0.50
rad/s at a constant angular acceleration of 0.20 rad/s2 for 1.0s?
Pg 259 Section Review
1. Find the tangential speed of a ball swung at a constant angular speed of 5.0 rad/s on a rope that is 5.0 m
long.
2. If an object has a tangential acceleration of 10.0 m/s2, the angular speed will do which of the following?
a-decrease
b-stay the same
c-increase
3. Find the tangential acceleration of a person standing 9.5 m from the center of a spinning amusement-park
ride that has an angular acceleration of 0.15 rad/s2.
4. If a spinning amusement –park ride has an angular speed of 1.2 rad/s, what is the centripetal acceleration
of a person standing 12 m from the center of the ride?
Pg 265 Section Review
1. A roller coaster moves through a vertical loop at a constant speed, suspending its passengers upside
down. In what direction is the force that causes the coaster and its passengers to move in a circle? What
provides this force?
2. Identify the force that maintains the circular motion of the following:
a- a bicyclist moving around a flat circular track
b- a bicycle moving around a flat circular track
c- a rubber stopper swung in a horizontal circle on its chain
d- a bobsled turning a corner on its track
3. A 90.0 kg person stands 1.00 m from a 60.0 kg person sitting on a bench nearby. What is the magnitude
of the gravitational force between them?
3. A 90.0 kg person rides a spinning amusement-park ride that has an angular speed of 1.15 rad/s. If the
radius of the ride is 11.5 m, what is the magnitude of the force that maintains the circular motion of the
person?
4. Calculate the mass that a planet with the same radius of Earth would need in order to exert the force on
the person in item 3 above.
Pg 269 Review
1. How many degrees equal π radians? How many revolutions?
2. What units must be used for θ, w, and a in the kinematic equations for rotational motion listed in table 72?
3. Distinguish between linear speed and angular speed.
4. When a wheel rotates about a fixed axis, do all points on the wheel have the same angular speed?
5. What is the angular displacement of the red line in each of the cases in #5 on p269. (Assume the red line
starts from the horizontal black line.)
6. A wheel has a radius of 4.1 m. How far (in arc length) does a point on the circumference travel if the
wheel is rotated through angles of 35°, 35 rad, and 35 rev, respectively?
7. What is the magnitude of the angular speed, w, of the second hand of a clock? What is the angular
acceleration, a, of the second hand?
8. Find the average angular speed of the Earth about the sun in radians per second. (Hint: Remember the
Earth orbits the sun once every 365.25 days.)
11. A drill starts from rest. After 3.20 s of contestant angular acceleration, the drill turns at a rate of 2628 rad/s.
a- find the drill’s angular acceleration
b- determine the angle through which the drill rotates during this period.
14. When a wheel rotates about a fixed axis, do all the points on the wheel have the same tangential speed?
16. Describe the path of a moving body whose acceleration is constant in magnitude at all times and is
perpendicular to the velocity.
19. Can a car move around a circular racetrack so that it has a tangential acceleration but no centripetal
acceleration?
21. It has been suggested that rotating cylinders about 10.0 mi long and 5.0 mi in diameter should be placed
in space for future space colonies. The rotation would simulate gravity for the inhabitants of these colonies.
Explain the concept behind this proposal.
27. Why does the water remain in a pail that is whirled in a vertical path, as shown in figure 7-16?
28. Explain the difference between centripetal acceleration and angular acceleration.
35. Tarzan (m=85 kg) tries to cross a river by swinging from a 10.0 m long vine. His speed at the bottom of
the swing, just as he clears the water, is 8.0 m/s. Tarzan doesn’t know that the vine has a breaking strength
of 1.0 x 103 N. Does he make it safely across the river? Justify your answer.
36. Approximate the gravitational force of attraction between a 50.0 kg girls and a 60.0 kg boy if they are
sitting 2.50 m apart in physics class.
38b. A 515 kg roller-coaster car rolls down past point A and then up past point B, as shown in figure 7-17
on page 271. What is the maximum speed the vehicle can have at B for gravity to hold it on track?
40a. An airplane is flying in a horizontal circle at a speed of 105 m/s. The 80.0 kg pilot does not want his
centripetal acceleration to exceed 7.00 times free-fall acceleration. What is the minimum radius of the
circular path?
43. A 2.00 x 103 kg car rounds a circular turn of radius 20.0 m. If the road is flat and the coefficient of
static friction between the tires and the road is 0.70, how fast can the car go without skidding?
44. A 13,500 N car traveling at 50.0 km/h rounds a curve of radius 2.00 x 102 m. Find the following:
a. The centripetal acceleration of the car
b. the force that maintains centripetal acceleration
c. the minimum coefficient of static friction between the tires and the road that will allow the car to round
the curve safely
46. A copper block rests 30.0 cm from the center of a steel turntable. The coefficient of the static friction
between the block and the surface is 0.53. the turntable starts from rest and rotates with a constant angular
acceleration of 0.50 rad/s2. After what time interval will the block start to slip on the turntable? (Hint: the
normal force in this case equals the weight of the block.)
50. At what minimum speed must a roller coaster be traveling when upside down at the top of a circle if
the passengers are not to fall out? Assume a radius of curvature of 8.6 m.