Rotational Motion Quizzes: Test Your Understanding

Question 1

What unit is used to measure torque?

Accepted Answer

Newton-meters

Answer

Joules

Answer

Radians per second

Answer

Watts

Question 2

An object rotates about a fixed axis. Its angular velocity is constant. Which of the following quantities remains constant?

Accepted Answer

Angular momentum

Answer

Angular acceleration

Answer

Linear velocity

Answer

Kinetic energy

Question 3

A flywheel rotates with an initial angular velocity. A constant torque is applied to the flywheel in the direction of rotation. What will happen to its angular velocity?

Accepted Answer

It will increase.

Answer

It will decrease.

Answer

It will remain the same.

Answer

It will oscillate.

Question 4

Which of the following is NOT a condition for rolling motion?

Accepted Answer

The object slides on the surface.

Answer

Linear and angular velocities are related.

Answer

The point of contact between the object and surface has zero velocity.

Answer

The object rotates about its own axis.

Question 5

What is the SI unit of angular momentum?

Accepted Answer

Kilogram-meters squared per second

Answer

Newton-meters

Answer

Joule-seconds

Answer

Radian-seconds

Question 6

Which of the following is an example of rotational kinetic energy?

Accepted Answer

A spinning top

Answer

A moving car

Answer

A falling object

Answer

A vibrating string

Question 7

What is the relationship between the moment of inertia and the rotational inertia of an object?

Accepted Answer

Moment of inertia is directly proportional to rotational inertia.

Answer

Moment of inertia is inversely proportional to rotational inertia.

Answer

Moment of inertia is equal to rotational inertia.

Answer

There is no relationship between moment of inertia and rotational inertia.

Question 8

An object with a moment of inertia of 2 kg m² is rotating with an angular velocity of 10 rad/s. What is its angular momentum?

Accepted Answer

20 kg m²/s

Answer

10 kg m²/s

Answer

2 kg m²/s

Answer

1 kg m²/s

Question 9

Which of the following is NOT a factor affecting the moment of inertia of an object?

Accepted Answer

Density

Answer

Mass

Answer

Shape

Answer

Axis of rotation

Question 10

Which of the following is a unit of moment of inertia?

Accepted Answer

Kilogram meters squared

Answer

Newton meters

Answer

Joules

Answer

Radians

Question 11

Which of the following is the formula for angular momentum?

Accepted Answer

Moment of inertia × Angular velocity

Answer

Angular velocity × Moment of inertia

Answer

Moment of inertia ÷ Angular velocity

Answer

Angular velocity ÷ Moment of inertia

Question 12

A rotating object has a constant angular velocity. Which of the following statements is true about its angular acceleration?

Accepted Answer

It is zero.

Answer

It is constant.

Answer

It is increasing.

Answer

It is decreasing.

Question 13

Which of the following is a condition for rotational equilibrium?

Accepted Answer

Net torque acting on the object is zero

Answer

Linear momentum of the object is zero

Answer

Angular velocity of the object is constant

Answer

Moment of inertia of the object is constant

Question 14

A pulley system has a mechanical advantage of 5. If an input force of 100 N is applied, what is the output force?

Accepted Answer

500 N

Answer

20 N

Answer

50 N

Answer

100 N

Question 15

Which of the following factors does NOT affect the period of a physical pendulum?

Accepted Answer

Amplitude of the swing

Answer

Mass of the object

Answer

Length of the string

Answer

Gravitational acceleration

Question 16

Which of the following is the relationship between angular velocity and tangential velocity?

Accepted Answer

v = ωr

Answer

ω = vr

Answer

v = rω

Answer

ω = v/r

Question 17

In a gyroscope, the precession of the axis of rotation is caused by:

Accepted Answer

External torque

Answer

Conservation of angular momentum

Answer

Gravity

Answer

Friction

Question 18

An object rotating about a fixed axis has an angular velocity of 10 radians per second. What is its angular displacement after 5 seconds?

Accepted Answer

50 radians

Question 19

The angular momentum of a system remains constant if:

Accepted Answer

No external torque acts on the system

Answer

The system is closed

Question 20

A flywheel has a moment of inertia of 5 kg-m^2. If it is rotating at an angular velocity of 10 rad/s, what is its kinetic energy?

Accepted Answer

125 J

Answer

50 J

Question 21

The moment of inertia of a thin rod of length L about an axis perpendicular to its midpoint is:

Accepted Answer

mL^2/12

Answer

mL^2/4

Question 22

The moment of inertia of a rigid body is influenced by:

Accepted Answer

Both mass and distribution of mass

Answer

Mass of the body

Answer

Distribution of mass within the body

Answer

Rotational speed of the body

Question 23

What is the SI unit of torque?

Accepted Answer

Newton-meter

Answer

Kilogram-meter

Answer

Joule

Answer

Watt

Question 24

The angular momentum of a rotating object is given by:

Accepted Answer

Moment of inertia multiplied by angular velocity

Answer

Torque multiplied by time

Answer

Mass multiplied by linear velocity

Answer

Radius multiplied by angular velocity

Question 25

Which condition is necessary for equilibrium in rotational motion?

Accepted Answer

Net torque acting on the object is zero

Answer

Net force acting on the object is zero

Answer

Object is at rest

Answer

Object is moving with a constant velocity

Question 26

A wheel rolls down an inclined plane without slipping. The acceleration of the wheel's center of mass is:

Accepted Answer

g sin θ

Answer

g cos θ

Answer

g

Answer

0

Question 27

In a torque-angle graph, what physical quantity does the area under the curve represent?

Accepted Answer

Work done by the torque

Answer

Power transmitted by the torque

Answer

Moment of inertia of the object

Answer

Angular velocity of the object

Question 28

Which of the following describes a fundamental property of rotational motion?

Accepted Answer

The torque applied to an object is directly proportional to the rate of change in its angular momentum.

Accepted Answer

The moment of inertia of an object quantifies its resistance to alterations in angular velocity.

Answer

Rotational motion solely occurs when an object spins around a fixed axis.

Question 29

A uniform rod of mass M and length L is pivoted at one end. The rod is released from rest at an angle θ from the vertical. What is the angular acceleration of the rod?

Accepted Answer

g sin(θ) / L

Answer

g cos(θ) / L

Answer

g / L

Answer

2g / L

Question 30

A particle of mass m is moving in a circular path of radius r with speed v. What is the magnitude of the particle's angular momentum about the center of the circle?

Accepted Answer

mvr

Answer

2mvr

Answer

3mvr

Answer

4mvr

Question 31

A flywheel of moment of inertia I is rotating with angular velocity ω. A constant torque τ is applied to the flywheel. What is the time taken for the flywheel to come to rest?

Accepted Answer

Iω / τ

Answer

2Iω / τ

Answer

3Iω / τ

Answer

4Iω / τ

Question 32

A thin rod of length L and mass M is pivoted at one end. A force F is applied perpendicular to the rod at a distance d from the pivot. What is the torque about the pivot due to the force?

Accepted Answer

Fd

Answer

2Fd

Answer

3Fd

Answer

4Fd

Question 33

A particle of mass m is moving in a circular path of radius r with speed v. The centripetal force acting on the particle is:

Accepted Answer

mv²/r

Answer

2mv²/r

Answer

3mv²/r

Answer

4mv²/r

Question 34

Two masses, m1 and m2, are connected by a light inextensible string that passes over a frictionless pulley. The system is released from rest. What is the acceleration of the masses?

Accepted Answer

(m1 - m2)g / (m1 + m2)

Answer

(m1 + m2)g / (m1 - m2)

Answer

g / 2

Answer

2g

Question 35

A rigid body is rotating with angular velocity ω. The radius of gyration of the body is k. What is the kinetic energy of the body?

Accepted Answer

½Iω²

Answer

Iω²

Answer

2Iω²

Answer

3Iω²

Question 36

In rotational motion, what is the primary significance of moment of inertia?

Accepted Answer

It quantifies an object's resistance to changes in rotational motion.

Answer

It simplifies calculations involving angular momentum.

Answer

It has no relevance in the study of rotational dynamics.

Question 37

When is a rigid body considered to be in torque equilibrium?

Accepted Answer

When the net torque acting on the body is zero

Answer

When the net force acting on the body is zero

Answer

When the angular velocity of the body remains constant

Answer

When the body is stationary with zero rotation

Question 38

Which of the following units is used to measure torque?

Accepted Answer

Nm

Answer

J

Answer

kgm^2

Answer

Nm/s

Question 39

In a rotational system, which physical quantity is conserved?

Accepted Answer

Angular momentum

Answer

Power

Answer

Linear momentum

Answer

Energy

Question 40

A force of 10N is applied to a rotating object at a distance of 2m from the axis of rotation. What is the torque produced by the force?

Accepted Answer

20 Nm

Answer

10 Nm

Answer

5 Nm

Answer

40 Nm

Question 41

A gyroscope is a device that uses the conservation of angular momentum to maintain its orientation. Which of the following is a characteristic of a gyroscope?

Accepted Answer

It resists changes in its axis of rotation.

Answer

It rotates at a constant speed.

Answer

It always points north.

Answer

It is used to measure time.

Question 42

A solid cylinder of mass M and radius R rolls down an inclined plane without slipping. What is the acceleration of the cylinder down the incline?

Accepted Answer

g(sin θ - μcos θ)

Answer

g(cos θ - μsin θ)

Answer

g(cos θ + μsin θ)

Answer

g(sin θ + μcos θ)

Question 43

A uniform disc of mass M and radius R is rotating about a fixed axis perpendicular to its plane. If the disc is acted upon by a constant torque τ for a time t, what is the work done on the disc?

Accepted Answer

½τt

Answer

¼τt

Answer

4τt

Answer

τt

Question 44

A rigid body is rotating about a fixed axis with angular velocity ω. Which of the following is a necessary condition for the body to be in equilibrium?

Accepted Answer

The net torque acting on the body is zero.

Answer

The net force acting on the body is zero.

Answer

The acceleration of the center of mass of the body is zero.

Answer

The kinetic energy of the body is constant.

Question 45

A wheel of radius 'R' rolls without slipping. Its linear velocity 'v' is related to its angular velocity 'ω' by:

Accepted Answer

v = Rω

Answer

v = 2Rω

Answer

v = Rω²

Question 46

A force 'F' is applied at a distance 'r' from the axis of rotation of a body. Calculate the torque acting on the body.

Accepted Answer

F × r

Answer

F - r

Answer

F + r

Answer

r × F

Question 47

A flywheel of moment of inertia 'I' has an initial angular velocity 'ω'. If a constant torque 'τ' is applied for time 't', determine the final angular velocity of the flywheel.

Accepted Answer

ω + (τt / I)

Answer

ω - (τt / I)

Answer

2ω + (τt / I)

Question 48

Identify the SI unit of angular momentum.

Accepted Answer

kg m²/s

Answer

kg m²

Answer

kg m/s

Question 49

A gyroscope has a large moment of inertia. This implies that it:

Accepted Answer

Resists changes in its orientation

Answer

Becomes less stable when spinning

Answer

Starts and stops rotating quickly

Question 50

A uniform rod of length 2m and mass 10kg is pivoted at its center. A force of 5N is applied perpendicularly to the rod at one end. What is the magnitude of the torque produced?

Accepted Answer

5 Nm

Answer

2.5 Nm

Answer

20 Nm

Answer

10 Nm

Question 51

A spinning ice skater pulls their arms in close to their body. What happens to their angular velocity?

Accepted Answer

Increases

Answer

Decreases

Answer

Cannot be determined

Answer

Stays the same

Question 52

A wheel rotates with an angular acceleration of 2 rad/s². If the initial angular velocity is 5 rad/s, what is the angular velocity after 3 seconds?

Accepted Answer

11 rad/s

Answer

6 rad/s

Answer

21 rad/s

Answer

15 rad/s

Question 53

A solid sphere and a hollow sphere, both of equal mass and radius, are released from rest at the top of an inclined plane. Which sphere reaches the bottom first?

Accepted Answer

Solid sphere

Answer

Both reach at the same time

Answer

Hollow sphere

Answer

Depends on the angle of inclination

Question 54

A merry-go-round is rotating at a constant angular speed. A child sitting on the edge of the merry-go-round experiences a centripetal acceleration of 4 m/s². If the radius of the merry-go-round is 2 meters, what is the angular speed of the merry-go-round?

Accepted Answer

1 rad/s

Answer

8 rad/s

Answer

2 rad/s

Answer

4 rad/s

Question 55

A disc rotates about an axis perpendicular to its plane and passing through its center. The moment of inertia of the disc is I. If the disc is divided into two equal parts, each part having half the mass of the original disc, what is the moment of inertia of each part?

Accepted Answer

I/4

Answer

2I

Answer

I

Answer

I/2

Question 56

A rotating object has a constant angular acceleration. Which of the following quantities is NOT constant?

Accepted Answer

Angular velocity

Answer

Angular acceleration

Answer

Angular displacement

Answer

Torque

Question 57

A wheel of radius 0.5 meters is rotating at a constant angular speed of 10 rad/s. What is the linear speed of a point on the rim of the wheel?

Accepted Answer

5 m/s

Answer

20 m/s

Answer

10 m/s

Answer

2.5 m/s

Question 58

A rigid body is rotating about a fixed axis. Which of the following statements is TRUE?

Accepted Answer

All points on the body have the same angular velocity

Answer

All points on the body have the same acceleration

Answer

All points on the body have the same linear velocity

Question 59

A flywheel is rotating at 120 revolutions per minute. What is its angular speed in radians per second?

Accepted Answer

4π rad/s

Answer

6π rad/s

Answer

12π rad/s

Answer

2π rad/s