Rigid Body Dynamics: Master the Motion of Solid Objects

Question 1

What is the primary function of a flywheel in mechanical systems?

Accepted Answer

Store energy

Answer

Reduce vibrations

Answer

Change the direction of rotation

Answer

Increase torque

Question 2

Which formula expresses the kinetic energy of a rotating rigid body?

Accepted Answer

(1/2)Iω^2

Answer

Iω^2

Answer

ω^2/I

Answer

(1/2)ω^2/I

Question 3

Which unit is employed to measure moment of inertia?

Accepted Answer

kg-m^2

Answer

kg-m

Answer

N-m

Answer

J-s

Question 4

What equation defines the condition of rotational equilibrium?

Accepted Answer

ΣM = 0

Answer

ΣF = 0

Answer

Σω = 0

Answer

Σα = 0

Question 5

Which factor has no influence on the moment of inertia of a rigid body?

Accepted Answer

Linear velocity

Answer

Mass

Answer

Mass distribution

Answer

Angular velocity

Question 6

State the conservation of angular momentum theorem for rigid bodies.

Accepted Answer

For a rigid body, the total angular momentum of the system remains constant if no external torque acts on the body.

Answer

Angular momentum is only conserved in deformable bodies.

Answer

Angular momentum of a rotating body is solely determined by its mass.

Answer

Angular momentum is always conserved in rotating systems, regardless of external influences.

Question 7

A solid sphere rolls down an inclined plane without slipping.  Using the work-energy principle, determine the sphere's equation of motion and the work done by friction. The sphere has mass *m*, radius *R*, and the incline has an angle *θ*.

Accepted Answer

Equation of Motion: $$Iα = mgsin(θ) - fR$$, Work Done by Friction: $$W_f = - fRθ$$

Answer

Equation of Motion: $$Iα = mgsin(θ) + fR$$, Work Done by Friction: $$W_f = 0$$

Answer

Equation of Motion: $$α = mgsin(θ) - fR$$, Work Done by Friction: $$W_f = - fR^2$$

Answer

Equation of Motion: $$α = mgsin(θ) + fR$$, Work Done by Friction: $$W_f = 0$$

Question 8

Which of the following is NOT a factor that affects the moment of inertia of a rigid body?

Accepted Answer

Temperature

Answer

Mass

Answer

Shape

Answer

Axis of rotation

Question 9

Which of the following is a conservative force?

Accepted Answer

Gravity

Answer

Friction

Answer

Tension

Answer

Air resistance

Question 10

Which formula accurately expresses the relationship between the angular momentum of a rigid body and its moment of inertia?

Accepted Answer

Angular momentum = Moment of inertia × Angular velocity

Answer

Moment of inertia = Angular momentum/ Angular velocity

Answer

Angular momentum = Moment of inertia^2× Angular velocity

Answer

Moment of inertia = Angular momentum × Angular displacement

Question 11

Which equations represent the equations of motion for a rigid body, according to Newton-Euler equations?

Accepted Answer

F = ma and M = Iα

Answer

F = Iα and M = ma

Answer

F = ma and M = Iω

Answer

F = Iω and M = ma

Question 12

Lagrange's Equations: Role in Rigid Body Dynamics

Accepted Answer

Lagrange's equations are crucial for deriving equations of motion for rigid bodies.

Answer

Lagrange's equations are used to solve for energy conservation in rigid body dynamics.

Answer

Lagrange's equations can be used to determine eigenvalues of rigid bodies.

Answer

Lagrange's equations are not applicable to rigid body dynamics.

Question 13

A rigid body experiences both a force F and a torque T. How does its motion differ from a particle subjected solely to force F?

Accepted Answer

The rigid body exhibits both translational and rotational motion, while the particle only translates.

Answer

The rigid body accelerates more than the particle.

Answer

The rigid body moves slower than the particle.

Answer

The rigid body's motion is unaffected by torque T.

Question 14

In rigid body dynamics, how do the degrees of freedom relate to the number of independent equations of motion needed to describe a rigid body's motion?

Accepted Answer

Degrees of freedom equal the number of independent equations of motion.

Answer

Degrees of freedom determine the number of scalar equations of motion.

Answer

Equations of motion always exceed degrees of freedom.

Answer

Degrees of freedom do not affect equations of motion.

Question 15

In rigid body dynamics, which principle forms the basis for deriving equations of motion for rigid bodies subjected to external forces and moments?

Accepted Answer

Newton's Second Law

Answer

Principle of Virtual Work

Answer

Hamilton's Principle

Answer

Principle of Least Action

Question 16

The moment of inertia of a body about a particular axis depends on:

Accepted Answer

Mass distribution and the chosen axis of rotation.

Answer

Mass distribution only.

Answer

Axis of rotation only.

Answer

Material properties of the body.

Question 17

Which of the following is a conserved quantity in rigid body dynamics?

Accepted Answer

Angular momentum

Answer

Linear momentum

Answer

Energy

Answer

Velocity

Question 18

A flywheel is used to store energy in rotating systems. The energy stored in the flywheel is given by:

Accepted Answer

1/2 Iω^2

Answer

2Iω^2

Answer

1/4 Iω^2

Answer

Iω

Question 19

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

Accepted Answer

Iα = ΣM

Answer

s = ut + 1/2 at^2

Answer

v = u + at

Answer

F = ma

Question 20

A gyroscope is a device that uses the principle of:

Accepted Answer

Conservation of angular momentum

Answer

Newton's second law

Answer

Hooke's law

Answer

Conservation of energy

Question 21

Which of the following is a common application of rigid body dynamics?

Accepted Answer

Design of rotating machinery

Answer

Circuit analysis

Answer

Modeling of fluid flow

Answer

Analysis of bridges

Question 22

A rigid body rotates about a fixed axis with constant angular acceleration. Which of the following quantities remains constant?

Accepted Answer

Angular momentum

Answer

Angular velocity

Answer

Kinetic energy

Answer

Moment of inertia

Question 23

The work done by a torque acting on a rigid body equals the change in:

Accepted Answer

Kinetic energy

Answer

Angular momentum

Answer

Potential energy

Answer

Linear momentum

Question 24

Determine the kinetic energy of a rigid body rotating about a fixed axis:

Accepted Answer

(1/2)Iω^2

Answer

Iω^2

Answer

2Iω^2

Answer

(1/4)Iω^2

Question 25

Define the center of mass of a rigid body:

Accepted Answer

The point where the net external force acting on the body is zero

Answer

The point where the net torque acting on the body is zero

Answer

The point where the linear momentum of the body is zero

Question 26

The equation governing the motion of a rigid body in rotation is:

Accepted Answer

ΣM = Iα

Answer

ΣM = ma

Answer

ΣF = Iα

Answer

ΣF = ma

Question 27

Define the angular velocity of a rigid body:

Accepted Answer

The rate of change of angular displacement

Answer

The rate of change of linear displacement

Answer

The rate of change of linear velocity

Question 28

Define the angular acceleration of a rigid body:

Accepted Answer

The rate of change of angular velocity

Answer

The rate of change of linear displacement

Answer

The rate of change of linear velocity

Answer

The rate of change of angular displacement

Question 29

A rigid body is rotating about a fixed axis with a constant angular acceleration. What can you conclude about its angular velocity?

Accepted Answer

It increases linearly with time.

Answer

It decreases linearly with time.

Answer

It remains constant.

Question 30

The moment of inertia of a body about an axis describes its:

Accepted Answer

Resistance to angular acceleration.

Answer

Gravitational force acting on it.

Answer

Gravitational potential energy.

Answer

Resistance to linear acceleration.

Question 31

Kinetic energy is a:

Accepted Answer

Scalar quantity.

Answer

Vector quantity.

Answer

Pseudo-vector quantity.

Answer

Tensor quantity.

Question 32

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

Accepted Answer

Equal to the resulting change in its rotational kinetic energy.

Answer

Equal to the resulting change in its potential energy.

Answer

Equal to the resulting change in its momentum.

Answer

Equal to the resulting change in its linear kinetic energy.

Question 33

Rolling motion is best defined as a combination of:

Accepted Answer

Translation and rotation.

Answer

Translation and vibration.

Answer

Rotation and oscillation.

Answer

Oscillation and vibration.

Question 34

Which of the following analytical methods is most appropriate for solving problems in rigid body dynamics?

Accepted Answer

Newton-Euler equations.

Answer

Maxwell's equations.

Answer

Navier-Stokes equations.

Answer

Einstein's field equations.

Question 35

A rigid body is suspended from a fixed point by a cable. The tension in the cable is:

Accepted Answer

Equal to the weight of the body.

Answer

Less than the weight of the body.

Answer

Zero.

Answer

Greater than the weight of the body.

Question 36

A common application of rigid body dynamics can be found in the design of:

Accepted Answer

Robotic arms.

Answer

Weather forecasting models.

Answer

Fluid flow systems.

Answer

Electronic circuits.

Question 37

A rigid body with angular velocity ω rotates about a fixed axis. If the torque acting on it is doubled, what will be its angular acceleration?

Accepted Answer

2ω

Answer

1/2ω

Answer

ω

Question 38

Which of the following conservation laws is not applicable to rigid body dynamics?

Accepted Answer

Conservation of linear velocity

Answer

Conservation of mass

Answer

Conservation of energy

Answer

Conservation of angular momentum

Question 39

Which theorem relates the linear and angular velocities of a rolling disk?

Accepted Answer

No-slip condition

Answer

Euler's theorem

Answer

Work-energy theorem

Answer

Pythagorean theorem

Question 40

A rigid body undergoes pure translation. What is the angular momentum of the body?

Accepted Answer

Zero

Answer

Cannot be determined

Answer

Non-zero and changing

Answer

Non-zero and constant

Question 41

Which of the following is a gyroscopic effect?

Accepted Answer

Precession

Answer

Newton's third law

Answer

Friction

Answer

Centrifugal force

Question 42

A rigid body is moving with constant velocity. What is its acceleration?

Accepted Answer

Zero

Answer

Constant

Answer

Cannot be determined

Answer

Non-uniform

Question 43

A flywheel with a moment of inertia of 20 kg-m^2 rotates at an angular velocity of 10 rad/s. Determine the kinetic energy stored in the flywheel.

Accepted Answer

1000 J

Answer

500 J

Answer

1500 J

Answer

750 J

Question 44

A wheel rolls without slipping on a horizontal surface. Which statement accurately describes the relationship between its linear and angular velocities?

Accepted Answer

Linear velocity is directly proportional to angular velocity.

Answer

Linear velocity is inversely proportional to angular velocity.

Answer

Linear velocity is directly proportional to the square of angular velocity.

Question 45

Energy storage capacity of a flywheel can be increased by:

Accepted Answer

Increasing its moment of inertia

Answer

Reducing its rotational speed

Answer

Reducing its diameter

Answer

Using a lighter material

Question 46

Which principle is fundamental to the operation of a gyroscope?

Accepted Answer

Conservation of angular momentum

Answer

Law of gravitation

Answer

Conservation of linear momentum

Answer

Newton's second law of motion

Question 47

During pure translation of a rigid body, which quantity remains constant?

Accepted Answer

Linear momentum

Answer

Angular momentum

Answer

Kinetic energy

Answer

Potential energy

Question 48

The work done by a torque applied to a rigid body rotating about a fixed axis is given by:

Accepted Answer

τ × Δθ

Answer

E × Δv

Answer

P × Δt

Answer

F × Δx

Question 49

A wheel rotates at a constant angular velocity. What is the relationship between the linear velocity of a point on the rim of the wheel and the radius of the wheel?

Accepted Answer

Linear velocity is directly proportional to the radius.

Answer

Linear velocity is zero.

Answer

Linear velocity is independent of the radius.

Answer

Linear velocity is inversely proportional to the radius.

Question 50

A torque is applied to a rotating object, causing a change in its angular momentum. How are torque and the change in angular momentum related?

Accepted Answer

Torque is equal to the rate of change of angular momentum.

Answer

Torque is proportional to the square of the change in angular momentum.

Answer

Torque is inversely proportional to the change in angular momentum.

Answer

There is no relationship between torque and the change in angular momentum.

Question 51

A solid cylinder rolls without slipping down an incline. Which of the following energy transformations does NOT occur?

Accepted Answer

Elastic potential energy to kinetic energy

Answer

Potential energy to translational kinetic energy

Answer

Gravitational potential energy to kinetic energy

Answer

Gravitational potential energy to rotational kinetic energy

Question 52

Two objects have the same mass. Object A has a larger moment of inertia than object B. Which object is more difficult to rotate?

Accepted Answer

Object A

Answer

It depends on the shape of the objects

Answer

They are equally difficult to rotate

Answer

Object B

Question 53

A spinning top remains upright due to:

Accepted Answer

Gyroscopic precession

Answer

Conservation of linear momentum

Answer

Centripetal force

Answer

Torque

Question 54

A uniform rod is pivoted at its center. Two forces of equal magnitude but opposite directions are applied perpendicular to the rod, at equal distances from the pivot. What is the net torque on the rod?

Accepted Answer

Zero

Answer

Twice the magnitude of one of the forces times the distance from the pivot

Answer

It depends on the angular velocity of the rod

Answer

The magnitude of one of the forces divided by the distance from the pivot