Master Rigid Body Motion: Online Quizzes for Engineering Mechanics

Question 1

A flywheel with a moment of inertia of 20 kg-m² is rotating at 100 rad/s. What is the kinetic energy stored in the flywheel?

Accepted Answer

1000 J

Answer

100 J

Answer

10 J

Answer

1 J

Question 2

A rigid body is in equilibrium under the action of three forces. What can be concluded?

Accepted Answer

Both (a) and (b) are true.

Answer

The resultant force acting on the body is zero.

Answer

The resultant moment about any point is zero.

Answer

Neither (a) nor (b) is true.

Question 3

A disk of radius 0.5 m rolls without slipping. If the linear velocity of the disk's center is 2 m/s, what is its angular velocity?

Accepted Answer

2 rad/s

Answer

1 rad/s

Answer

4 rad/s

Answer

8 rad/s

Question 4

A particle moves in a circular path of radius 10 m. If the particle completes one revolution in 20 seconds, what is its angular velocity?

Accepted Answer

π rad/s

Answer

2π rad/s

Answer

0.5π rad/s

Answer

0.25π rad/s

Question 5

A force of F = 10 N is applied to a body of mass 2 kg at an angle of 30° with the horizontal. What is the work done by the force over a displacement of 5 m?

Accepted Answer

43.3 J

Answer

25 J

Answer

50 J

Answer

75 J

Question 6

A rigid body is rotating about a fixed axis with an angular velocity of 10 rad/s. If a constant torque is applied to the body, what type of motion does it cause?

Accepted Answer

The body will accelerate with constant angular acceleration.

Answer

The body will continue to rotate with constant angular velocity.

Answer

The body will decelerate with constant angular acceleration.

Answer

The body will stop rotating.

Question 7

The work done by a constant force F on a rigid body moving with a displacement r is given by:

Accepted Answer

W = Fr cosθ

Answer

W = F/r

Answer

W = rF

Answer

W = F^2/r

Question 8

A rigid body is in rotational equilibrium if:

Accepted Answer

The sum of the moments of the forces acting on the body about any point is zero.

Answer

The sum of the forces acting on the body is zero.

Question 9

The angular momentum of a rigid body is a conserved quantity if:

Accepted Answer

The net torque acting on the body is zero.

Answer

The linear momentum of the body is constant.

Question 10

Which of the following is the SI unit of angular velocity?

Accepted Answer

radians per second

Answer

meters per second

Question 11

The angular acceleration of a rotating object is directly proportional to which quantity?

Accepted Answer

Net torque applied

Answer

Moment of inertia

Answer

Angular velocity

Answer

Mass of the body

Question 12

Impulse acting on an object is defined as:

Accepted Answer

Change in momentum

Answer

Force applied for a certain time

Answer

Mass multiplied by velocity

Answer

Work done on the body

Question 13

A rigid body is said to be in equilibrium when:

Accepted Answer

The sum of forces acting on it is zero

Answer

The sum of forces acting on it is non-zero

Answer

The sum of forces acting on it is equal to its weight

Answer

The sum of forces acting on it is equal to its mass

Question 14

The moment of inertia of a body about a given axis is:

Accepted Answer

A measure of the body's resistance to angular acceleration

Answer

A measure of the body's mass

Answer

A measure of the body's velocity

Answer

A measure of the body's force

Question 15

The angular velocity of a body is defined as:

Accepted Answer

Rate of change of angular displacement

Answer

Rate of change of angular acceleration

Answer

Rate of change of velocity

Answer

Rate of change of momentum

Question 16

A torque of 100 Nm is applied to a flywheel with a moment of inertia of 20 kg-m^2. What is the resulting angular acceleration of the flywheel?

Accepted Answer

5 rad/s^2

Answer

10 rad/s^2

Answer

2.5 rad/s^2

Answer

20 rad/s^2

Question 17

The equation of motion for a rigid body with constant mass and acceleration is: *

Accepted Answer

F = ma

Answer

F = ma + W

Answer

F = mv

Answer

F = 0

Question 18

Which of the following is the formula for work done by a force? *

Accepted Answer

W = Fd

Answer

W = Fvt

Answer

W = F/d

Answer

W = mv^2

Question 19

The impulse imparted to a rigid body equals to: *

Accepted Answer

The change in momentum

Answer

The work done on the body

Answer

The force applied to the body

Answer

The kinetic energy of the body

Question 20

Which of the following is NOT a type of moment of inertia? *

Accepted Answer

Time moment of inertia

Answer

Mass moment of inertia

Answer

Area moment of inertia

Answer

Volume moment of inertia

Question 21

The equation for rotational kinetic energy is: *

Accepted Answer

K = 1/2 I ω^2

Answer

K = I ω

Answer

K = 1/2 m v^2

Answer

K = m v

Question 22

The angular velocity of a rigid body is: *

Accepted Answer

The rate of change of angular displacement

Answer

The product of linear velocity and angular displacement

Answer

The cross product of linear velocity and angular displacement

Answer

The derivative of linear velocity with respect to time

Question 23

The acceleration of a point moving in a circle is: *

Accepted Answer

a = ω^2r

Answer

a = rω^2

Answer

a = ω/r

Answer

a = r/ω

Question 24

A rigid body initially at rest rotates about a fixed axis with a constant angular acceleration of 2 rad/s². What is its angular velocity after 5 seconds?

Accepted Answer

10 rad/s

Answer

5 rad/s

Answer

20 rad/s

Answer

1 rad/s

Question 25

A rigid body is subjected to a moment of inertia I about a fixed axis. If a torque τ acts on the body, what is its angular acceleration?

Accepted Answer

τ/I

Answer

I/τ

Answer

τI

Answer

Iτ

Question 26

A flywheel with a moment of inertia I rotates with an angular velocity ω. If the flywheel experiences a constant torque τ for a time t, what is its final angular velocity?

Accepted Answer

ω + (τt/I)

Answer

ω - (τt/I)

Answer

(τt)/I

Answer

ω

Question 27

A series of forces F1, F2, ..., Fn act on a rigid body. What is the resultant force acting on the body?

Accepted Answer

ΣF1 + ΣF2 + ... + ΣFn

Answer

ΣF1 - ΣF2 - ... - ΣFn

Answer

√(ΣF1^2 + ΣF2^2 + ... + ΣFn^2)

Answer

0

Question 28

What is the definition of angular velocity for a rigid body?

Accepted Answer

Rate of change of angular displacement over time

Answer

Rate of change of linear displacement over time

Answer

Rate of change of angular momentum over time

Answer

Rate of change of linear momentum over time

Question 29

The impulse acting on a rigid body subjected to a constant force F for a time interval t is:

Accepted Answer

Ft

Answer

F/t

Answer

Ft^2

Answer

F/t^2

Question 30

The center of mass of a rigid body:

Accepted Answer

Is a fixed point within the body

Answer

Coincides with the geometric center of the body

Answer

Can shift as the body moves

Answer

Depends on the reference frame

Question 31

The moment of inertia of a rigid body about an axis is a measure of its:

Accepted Answer

Resistance to angular acceleration

Answer

Resistance to linear acceleration

Answer

Resistance to deformation

Answer

Resistance to shear forces

Question 32

The law of conservation of angular momentum states that:

Accepted Answer

The total angular momentum of a system remains constant if no external torque acts on the system

Answer

The total angular momentum of a system is proportional to its kinetic energy

Answer

The angular momentum of a system is conserved only if the system is rotating at a constant speed

Answer

The angular momentum of a system is conserved only if the system is in equilibrium

Question 33

A rigid body is in plane motion. The velocity of its center of mass is v and its angular velocity is ω. The velocity of a point on the body at a distance r from the center of mass is:

Accepted Answer

v + ωr

Answer

v - ωr

Answer

|v + ωr|

Answer

ωr

Question 34

The kinetic energy of a rigid body rotating about a fixed axis is:

Accepted Answer

(1/2)Iω^2

Answer

Iω

Answer

Iω^2

Answer

ω/I

Question 35

The work done by a torque acting on a rigid body is:

Accepted Answer

Equal to the torque times the angular displacement of the body

Answer

Equal to the change in rotational kinetic energy of the body

Answer

Equal to the torque times the angular velocity of the body

Answer

Independent of the angular displacement of the body

Question 36

The radius of gyration of a rigid body about an axis is a measure of its:

Accepted Answer

Mass distribution

Answer

Shape

Answer

Density

Answer

Volume

Question 37

A block of mass 2 kg is pushed across a rough surface by a force of 10 N. If the coefficient of kinetic friction between the block and the surface is 0.2, what is the acceleration of the block?

Accepted Answer

4 m/s²

Answer

2 m/s²

Answer

6 m/s²

Answer

8 m/s²

Question 38

The work done by a force on a rigid body is equal to the:

Accepted Answer

Product of force and displacement in the direction of the force

Answer

Product of force and velocity

Answer

Product of force and acceleration

Answer

Product of force and momentum

Question 39

The impulse acting on a rigid body is numerically equal to the:

Accepted Answer

Change in momentum

Answer

Change in kinetic energy

Answer

Change in potential energy

Answer

Change in velocity

Question 40

The angular momentum of a rigid body about an axis is equal to the:

Accepted Answer

Product of moment of inertia and angular velocity

Answer

Product of mass and angular velocity

Answer

Product of force and angular displacement

Answer

Product of torque and angular acceleration

Question 41

The impulse-momentum theorem for a rigid body states that the net impulse acting on the body is equal to the:

Accepted Answer

Change in linear momentum

Answer

Change in angular momentum

Answer

Sum of its linear and angular momentums

Answer

Mass times its acceleration

Question 42

The kinetic energy of a rolling body is equal to the:

Accepted Answer

Sum of its translational and rotational kinetic energies

Answer

Difference between its translational and rotational kinetic energies

Answer

Product of its mass and its velocity squared

Answer

Half of its mass and its velocity squared

Question 43

A rigid body is in equilibrium if the net force and net moment acting on it are both:

Accepted Answer

Zero

Answer

Non-zero

Answer

Equal

Answer

Opposite

Question 44

The impulse acting on a rigid body is equal to the:

Accepted Answer

Change in momentum

Answer

Change in kinetic energy

Answer

Force acting on the body

Answer

Time for which the force acts

Question 45

The moment of inertia of a body depends on:

Accepted Answer

Mass distribution and axis of rotation

Answer

Shape and density

Answer

Volume and surface area

Answer

Material properties

Question 46

The equation of motion for a rigid body in plane motion is:

Accepted Answer

ΣF = 0, ΣM = 0

Answer

F = ma

Answer

a = v/t

Answer

s = ut + 1/2 at^2

Question 47

The coefficient of restitution is a measure of:

Accepted Answer

Elasticity of a collision

Answer

Inelasticity of a collision

Answer

Momentum of a collision

Answer

Energy of a collision

Question 48

The kinetic energy of a rigid body in pure rotation is:

Accepted Answer

1/2 Iω^2

Answer

Iω^2

Answer

1/2 mω^2

Answer

mω^2

Question 49

A wheel rolls without slipping on a horizontal surface. If its center has a linear velocity of v, what is its angular velocity?

Accepted Answer

ω = v/r

Answer

ω = 2v/r

Answer

ω = v/2r

Question 50

A rigid body is subjected to a constant force. Which of the following statements correctly describes the relationship between the force, the body's mass (m), and its linear acceleration (a)?

Accepted Answer

F = ma

Answer

F = ma/2

Answer

F = 2ma

Question 51

A rigid body undergoes pure translation. Which of the following statements correctly describes the motion of its constituent particles?

Accepted Answer

All particles have the same velocity and acceleration.

Answer

All particles have the same velocity but different accelerations.

Answer

All particles have different velocities but the same acceleration.

Question 52

A system of particles is in equilibrium. Which of the following statements must be true?

Accepted Answer

The net force and the net moment acting on the system are both zero.

Answer

The net force acting on the system is zero only.

Answer

The net moment acting on the system is zero only.

Question 53

A rigid body is subjected to a series of impulsive forces. Which of the following quantities remains constant during the impulsive loading?

Accepted Answer

Momentum

Answer

Kinetic energy

Answer

Angular velocity

Answer

Velocity

Question 54

A rigid body rotates about a fixed axis with constant angular velocity. Which of the following is true about its moment of inertia?

Accepted Answer

It is constant with respect to the axis of rotation.

Answer

It increases with the angular velocity.

Answer

It decreases with the angular velocity.

Question 55

A rigid body is subjected to a torque. Which of the following statements correctly describes the resulting angular acceleration?

Accepted Answer

It is directly proportional to the torque and inversely proportional to the moment of inertia.

Answer

It is independent of both the torque and the moment of inertia.

Answer

It is inversely proportional to the torque and directly proportional to the moment of inertia.

Question 56

Which of the following is a valid expression for the work done by a force acting on a rigid body undergoing pure translation?

Accepted Answer

W = F · d

Answer

W = F · α

Answer

W = F · t

Answer

W = F · v