Dynamics of Rigid Bodies: Master the Motion and Forces of Rotating and Translating Objects

Question 1

The linear momentum of a 5 kg object is 10 kg-m/s. What is its velocity?

Accepted Answer

2 m/s

Answer

1 m/s

Answer

3 m/s

Answer

4 m/s

Question 2

A rigid body rotates with a constant angular velocity ω about a fixed axis. How does the body's angular momentum relate to its angular velocity and moment of inertia?

Accepted Answer

Angular momentum is directly proportional to both angular velocity (ω) and moment of inertia.

Answer

Angular momentum is proportional to the square of angular velocity (ω^2) and the body's mass.

Answer

Angular momentum remains constant in both magnitude and direction for a rotating rigid body.

Answer

Angular momentum is a scalar quantity, possessing only magnitude and no direction.

Question 3

Which of the following equations represents Newton's second law for rotational motion?

Accepted Answer

T = Iα

Answer

F = ma

Answer

W = Fd

Answer

P = FV

Question 4

A flywheel with radius R is rotating at angular velocity ω. What is the linear velocity of a point on the rim of the flywheel?

Accepted Answer

Rω

Answer

2Rω

Answer

Rω/2

Answer

ω/R

Question 5

A rigid body rotates with a constant angular velocity about a fixed axis. Which quantity is **not** conserved?

Accepted Answer

Linear momentum

Answer

Angular momentum

Answer

Kinetic energy

Answer

Angular velocity

Question 6

A wheel of mass m and radius R rolls without slipping on a horizontal surface with a center of mass velocity v. What is the magnitude of the wheel's angular velocity?

Accepted Answer

v/R

Answer

2v/R

Answer

v/2R

Answer

3v/2R

Question 7

A particle travels in a circular path of radius r at constant speed v. The centripetal acceleration of the particle is:

Accepted Answer

v^2/r

Answer

v/r

Answer

2v^2/r

Answer

Zero

Question 8

The kinetic energy of a rolling body is:

Accepted Answer

1/2mv^2 + 1/2Iω^2

Answer

mv^2 + Iω^2

Answer

1/2mv^2

Answer

1/2Iω^2

Question 9

The work done in lifting a body of mass m through a height h against the force of gravity is:

Accepted Answer

mgh

Answer

1/2mgh

Answer

2mgh

Answer

Zero

Question 10

A gyroscope is a device that utilizes the principle of:

Accepted Answer

Conservation of angular momentum

Answer

Conservation of linear momentum

Answer

Conservation of energy

Answer

Conservation of mass

Question 11

A wheel rotating at 100 rpm undergoes a constant angular acceleration of 5 rad/s^2 for 10 seconds. What is its angular velocity at the end of this period?

Accepted Answer

250 rpm

Answer

150 rpm

Answer

200 rpm

Answer

300 rpm

Question 12

The principle of conservation of angular momentum states that:

Accepted Answer

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

Answer

The angular momentum of each individual body in a system remains constant

Answer

The total kinetic energy of a system remains constant

Answer

The total linear momentum of a system remains constant

Question 13

For a rigid body rotating about a fixed axis with angular velocity ω, the magnitude of its tangential velocity v at a distance r from the axis of rotation is:

Accepted Answer

v = ωr

Answer

v = ω / r

Answer

v = 2ωr

Answer

v = ω^2r

Question 14

The principle of conservation of angular momentum states that:

Accepted Answer

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

Answer

The total linear momentum of a system remains constant if no external force acts on it

Answer

The total energy of a system remains constant if no external work is done on it

Answer

The total mass of a system remains constant if no material is added or removed

Question 15

The SI units of moment of inertia are:

Accepted Answer

Kilogram meter squared (kg m^2)

Answer

Kilogram meter (kg m)

Answer

Newton meter (N m)

Answer

Newton meter squared (N m^2)

Question 16

Which of the following is NOT a fundamental principle of rigid body dynamics?

Accepted Answer

Statics

Answer

Kinematics

Answer

Kinetics

Answer

Energy methods

Question 17

The angular momentum of a rigid body is:

Accepted Answer

A vector quantity

Answer

A scalar quantity

Answer

A tensor quantity

Answer

A matrix quantity

Question 18

The equation of motion for a rigid body in rotation about a fixed axis is:

Accepted Answer

ΣM = Iα

Answer

ΣF = ma

Answer

v = u + at

Answer

s = ut + 0.5at^2

Question 19

The motion of a rolling object is a combination of:

Accepted Answer

Translation and rotation

Answer

Rotation and vibration

Answer

Translation and oscillation

Answer

Vibration and damping

Question 20

The gyroscopic effect is caused by:

Accepted Answer

The conservation of angular momentum

Answer

The law of gravity

Answer

The principle of buoyancy

Answer

The Bernoulli effect

Question 21

Which physical quantity is NOT a vector quantity?

Accepted Answer

Mass

Answer

Velocity

Answer

Displacement

Answer

Force

Question 22

In a pure rolling motion, the point of contact between the body and the surface has:

Accepted Answer

Zero linear velocity

Answer

Zero angular velocity

Answer

Non-zero linear and angular velocities

Answer

Both zero linear and angular velocities

Question 23

The principle of linear impulse and momentum states that the net external force acting on a rigid body is equal to the:

Accepted Answer

Rate of change of linear momentum

Answer

Linear momentum

Answer

Angular momentum

Answer

Kinetic energy

Question 24

The angular acceleration of a rigid body undergoing pure rotation is directly proportional to the:

Accepted Answer

Net torque

Answer

Moment of inertia

Answer

Mass

Answer

Radius of rotation

Question 25

The total energy of a closed system in rigid body dynamics is:

Accepted Answer

Conserved

Answer

Increased

Answer

Decreased

Answer

Zero

Question 26

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

Accepted Answer

Resistance to angular acceleration

Answer

Mass

Answer

Angular momentum

Answer

Kinetic energy

Question 27

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

Accepted Answer

Zero

Answer

Non-zero

Answer

Equal

Answer

Opposite

Question 28

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

Accepted Answer

Kinetic energy

Answer

Potential energy

Answer

Angular momentum

Answer

Linear momentum

Question 29

Which of the following is a characteristic of an optimally balanced flywheel?

Accepted Answer

It runs at a constant speed.

Answer

It has a small moment of inertia.

Answer

It stores potential energy.

Answer

It transmits power between shafts.

Question 30

The gyroscopic effect is due to the conservation of:

Accepted Answer

Angular momentum

Answer

Linear momentum

Answer

Energy

Answer

Mass

Question 31

The principle of superposition states that the motion of a rigid body can be analyzed as the combination of:

Accepted Answer

Translations and rotations

Answer

Forces and moments

Answer

Kinetic and potential energy

Answer

Linear and angular momentum

Question 32

Which of the following is NOT a fundamental principle of rigid body dynamics, as covered in this unit?

Accepted Answer

Fluid mechanics

Answer

Kinematics

Answer

Kinetics

Answer

Energy methods

Question 33

What is the equation of motion for a rigid body in rotational form, as covered in the section on rotational kinematics?

Accepted Answer

∑M = Iα

Answer

∑F = ma

Answer

W = Fs

Answer

KE = 1/2mv^2

Question 34

A rigid body is subjected to a constant force. Which of the following is NOT true about its motion, given its constant acceleration?

Accepted Answer

It will eventually reach a terminal velocity

Answer

It will have constant acceleration

Answer

Its velocity will increase linearly with time

Answer

Its displacement will increase quadratically with time

Question 35

What is the work done by a moment M acting through an angular displacement θ, as covered in the section on work in rotational systems?

Accepted Answer

Mθ

Answer

1/2Mθ

Answer

2Mθ

Answer

Mθ^2

Question 36

The principle of impulse and momentum states that the net impulse acting on a body is equal to what, as discussed in the section on impulse and momentum?

Accepted Answer

Change in linear momentum

Answer

Change in angular momentum

Answer

Force acting on the body

Answer

Displacement of the body

Question 37

A rigid body rotates about a fixed axis with angular velocity ω. What is the kinetic energy of the body?

Accepted Answer

1 / 2 Iω^2

Answer

Iω^2

Answer

2Iω^2

Answer

4Iω^2

Question 38

For a rigid body undergoing pure translation, which of these quantities will remain constant?

Accepted Answer

Linear momentum

Answer

Angular velocity

Answer

Angular acceleration

Answer

Linear acceleration

Question 39

When a rigid body is subjected to a constant torque, its angular acceleration:

Accepted Answer

Remains constant

Answer

Is zero

Answer

Increases with time

Answer

Decreases with time

Question 40

A flywheel's primary function is to:

Accepted Answer

Store kinetic energy

Answer

Reduce vibrations

Answer

Change the direction of motion

Answer

Amplify torque

Question 41

The gyroscopic effect is a result of:

Accepted Answer

Precession of a rotating rigid body

Answer

Nutation of a rotating rigid body

Answer

Centrifugal force acting on a rotating rigid body

Answer

Coriolis force acting on a rotating rigid body