circular and rotational motion

Question 1

An object moves in a circular path at a constant speed. Which of the following is true?

(a) The car’s acceleration is zero because it has a constant speed.
(b) The car’s acceleration is not zero and causes the car to decrease speed.
(c) The car’s acceleration is not zero and causes the car to increase speed.
(d) The car’s acceleration is not zero and causes the change in the direction of the car’s velocity.
(e) None of these is correct.

Answer 1

(a) The car’s acceleration is zero because it has a constant speed.

Question 2

An object moves around a circular path at a constant speed and makes five complete revolutions in 20 seconds. What is the period of rotation (time taken for one revolution)?
(a) 5 s
(b) 10 s
(c) 4 s
(d) 20 s
(e) 15 s

Answer 2

(c) 4 s

Question 3

A race car is traveling in uniform circular motion around a racetrack. What happens to the centripetal acceleration of the car if the speed is doubled but the radius of the circle remains constant?
(a) It remains the same.
(b) It increases by a factor of 2.
(c) It increases by a factor of 4.
(d) It is decreased by a factor of one-half.
(e) It is decreased by a factor of one-fourth.

Answer 3

(c) It increases by a factor of 4.

Question 4

A certain string breaks when it reaches a tension of 400 N. A boy uses this string to whirl a 10 kg stone in a horizontal circle of radius 10 m. The boy continuously increases the speed of the stone. At what speed will the string break? Assume the tension force is directed horizontally.
(a) 10 m/s
(b) 20 m/s
(c) 80 m/s
(d) 100 m/s
(e) 400 m/s

Answer 4

(b) 20 m/s

Question 5

Which force is responsible for holding a car in an unbanked curve?
(a) the car’s weight
(b) the force of friction
(c) the reaction force to the car’s weight
(d) the vertical component of the normal force
(e) the horizontal component of the normal force

Answer 5

(b) the force of friction

Question 6

A solid disk with a radius 𝑅 rotates at a constant rate 𝜔. Which of the following points has the greater angular velocity?
(a) A
(b) B
(c) C
(d) D
(e) All points have the same angular velocity

Answer 6

(e) All points have the same angular velocity

Question 7

A solid disk with a radius 𝑅 rotates at a constant rate 𝜔. Which of the following points has the greater linear velocity?

(a) A
(b) B
(c) C
(d) D
(e) All points have the same linear velocity

Answer 7

(a) A

Question 8

Two points A and C are on the disk that rotates about an axis. Point A is three times as far from the axis as point C. If the speed of point C is 𝑣, then what is the speed of point A?

(a) 𝑣
(b) 9𝑣
(c) v/3
(d) 3𝑣
(e) Sqroot (3v)

Answer 8

(d) 3𝑣

Question 9

What is the angular frequency of rotation of the Earth as it rotates about its axis (in rad/s)?
(a) π/12
(b) π/43,200
(c) 1 / 86,400
(d) 1 / 24
(e) none of (a) - (d)

Answer 9

(b) π/43,200

Question 10

The crankshaft in your car engine is turning at 3,000 rpm. What is the shaft’s angular speed?
(A) 4π rad/s
(B) 200π rad/s
(C) 50π rad/s
(D) 100π rad/s

Answer 10

(D) 100π rad/s

Question 11

A ball rolls around a circular track with an angular velocity of 4π rad/s. What is the period of the ball’s motion?
(A) 1 s
(B) 2 s
(C) 1/2 s
(D) π s
(E) 1/π s

Answer 11

(C) 1/2 s

Question 12

Rasheed and Sofia are riding a merry-go-round that is spinning steadily. Sofia is twice as far from the axis as is Rasheed. The ratio of Sofia’s angular velocity to that of Rasheed is:
(A) 1
(B) 2
(C) 1/2
(D) π
(E) 1/π

Answer 12

(A) 1

Question 13

Rasheed and Sofia are riding a merry-go-round that is spinning steadily. Sofia is twice as far from the axis as is Rasheed. The ratio of Sofia’s linear velocity to that of Rasheed is:
(A) 1
(B) 2
(C) 1/2
(D) π
(E) 1/π

Answer 13

(B) 2

Question 14

A turbine at a power plant is initially turning at a high rate. The steam supplied to it is turned off. What is the relative direction of the angular velocity and the angular acceleration?
(A) Parallel
(B) Opposite (or Antiparallel)
(C) Cannot say without knowing the radius of the blades

Answer 14

(B) Opposite (or Antiparallel)

Question 15

The scale is in the middle of the rod. What does it read?
(A) 500 N
(B) 1,000 N
(C) 2,000 N
(D) 4,000 N

Answer 15

(C) 2,000 N

Question 16

A cone balanced on its small end is in:
(A) stable equilibrium
(B) unstable equilibrium
(C) neutral equilibrium
(D) positive equilibrium
(E) negative equilibrium

Answer 16

(C) neutral equilibrium

Question 17

If the net force on an object is zero, then the net torque on the object also has to be zero. T or F

Answer 17

false

Question 18

An object whose center of gravity is below its point of support will be in neutral equilibrium. T or F

Answer 18

false

Question 19

If an object is in equilibrium, the net torque about any arbitrary axis must be zero. T or F

Answer 19

true

Question 20

If the net torque on an object is zero, then the net force on the object also has to be zero. T or F

Answer 20

false

Question 21

Given the force vs. time graph as shown calculate the change in the linear momentum from 20 to 30 milliseconds.

A. 0.200 kg·m/s
B. 0.300 kg·m/s
C. zero
D. Cannot be determined if the mass is not known.

Answer 21

A. 0.200 kg·m/s

Question 22

Two bodies of equal mass m collide and stick together. The quantities that always have equal magnitudes for both masses during the collision are:

A. Their changes in momentum.
B. Their changes in kinetic energy.
C. The force each exerts on the other.
D. All of these.
E. Only A and C.

Answer 22

E. Only A and C.

Question 23

A small sphere is attached to a light rigid rod which rotates about an axis perpendicular to and fixed to the other end of the rod. Initially, the angular position of the sphere is negative, its angular velocity is negative, and its angular acceleration is positive. The sphere is:

A. initially rotating clockwise and decreasing speed, and then rotating counterclockwise at increasing speed.
B. rotating clockwise and increasing speed.
C. rotating counterclockwise and decreasing speed.
D. rotating counterclockwise and increasing speed.
E. initially rotating counterclockwise and decreasing speed, and then rotating clockwise at increasing speed.

Answer 23

A. initially rotating clockwise and decreasing speed, and then rotating counterclockwise at increasing speed.

Question 24

A wheel rotating about a fixed axis has an angular displacement given by θ(t)=3.0−t^4, where t is in seconds and θ is in radians. What is the angular acceleration of the wheel at time t=2.0 seconds?

A. -13.0 rad/s²
B. -48.0 rad/s²
C. -12.0 rad/s²
D. -4.0 rad/s²
E. -32 rad/s²

Answer 24

B. -48.0 rad/s²

Question 25

In the figure, a small 1.6 kg mass swings in a vertical circle at the end of a string having negligible weight. The string is 2.0 m long. If the mass is released with zero initial velocity from a horizontal position, then its angular momentum at the lowest point of its path, measured relative to the center of the circle, will be:

A. 40 kg·m²/s
B. 10 kg·m²/s
C. 30 kg·m²/s
D. 20 kg·m²/s
E. 50 kg·m²/s

Answer 25

D. 20 kg·m²/s

Question 26

A particle located at the position vector r=(1+j) m, has a force F=(2i+3j) N acting on it. What is the torque about an axis located at the origin that is perpendicular to the page?

A. (+1k) m·N
B. (+5k) m·N
C. (−1k) m·N
D. (−5k) m·N
E. (+2i+3j) m·N

Answer 26

A. (+1k) m·N

Question 27

A small mass is whirled in a horizontal circle at the end of a light string 75 cm long at a linear speed of 3.0 m/s. If the string is lengthened to 1.5 m while the mass is still in motion, then the linear speed of the ball will be:

A. larger and have a smaller angular momentum.
B. larger and have a larger angular momentum.
C. smaller and have a smaller angular momentum.
D. smaller and have the same angular momentum.

Answer 27

D. smaller and have the same angular momentum.