Kinematics of Rigid Bodies: Master the Motion of Solid Objects

Question 1

The angular velocity of a rigid body is a:

Accepted Answer

Vector quantity with both magnitude and direction

Answer

Scalar quantity with both magnitude and direction

Answer

Vector quantity with only magnitude

Answer

Tensor quantity with only magnitude

Question 2

The acceleration of a point on a rotating rigid body is:

Accepted Answer

Always perpendicular to the radius vector from the point to the center of rotation

Answer

Always directed towards the center of rotation

Answer

Always directed away from the center of rotation

Answer

Can be either towards or away from the center of rotation

Question 3

The kinematics of rigid bodies is a branch of mechanics that deals with the:

Accepted Answer

Motion of bodies without considering the forces acting on them

Answer

Forces acting on bodies without considering their motion

Answer

Both motion and forces acting on bodies

Answer

Neither motion nor forces acting on bodies

Question 4

The velocity of a particle moving in a circle of radius 'r' with a constant angular velocity 'ω' is:

Accepted Answer

rω

Answer

rω²

Answer

½rω

Answer

¼rω²

Question 5

The acceleration of a particle moving in a circle of radius 'r' with a constant angular velocity 'ω' is:

Accepted Answer

rω²

Answer

rω

Answer

½rω

Answer

¼rω²

Question 6

A flywheel has a moment of inertia of 10 kg-m² and is rotating at an angular velocity of 100 rad/s. Its angular momentum is:

Accepted Answer

2000 kg-m²/s

Answer

1000 kg-m²/s

Answer

3000 kg-m²/s

Answer

4000 kg-m²/s

Question 7

A rigid body undergoes pure rotational motion about a fixed axis. Which of the following quantities remains constant?

Accepted Answer

Angular velocity

Answer

Angular acceleration

Answer

Linear velocity

Answer

Linear acceleration

Question 8

Which of the following is NOT a type of rigid body motion?

Accepted Answer

Deformation

Answer

Translation

Answer

Rotation

Answer

Vibration

Question 9

In the combined translational and rotational motion of a rigid body, which quantity remains constant?

Accepted Answer

Total angular momentum

Answer

Linear velocity of the center of mass

Answer

Kinetic energy

Answer

Rotational velocity of the body

Question 10

A rigid body has a moment of inertia of 5 kg-m^2 about a fixed axis. It is acted upon by a torque of 10 N-m. What is the resulting angular acceleration?

Accepted Answer

2 rad/s^2

Answer

1 rad/s^2

Answer

5 rad/s^2

Answer

10 rad/s^2

Question 11

A particle undergoes a motion described by the position vector r(t) = (3t^2, 2t) meters. What is the velocity of the particle?

Accepted Answer

(6t, 2) m/s

Answer

(3t, 2) m/s

Answer

(6t, 0) m/s

Answer

(3t, 0) m/s

Question 12

A rigid body is rotating about a fixed axis with a constant angular velocity. Which of the following is not true about the motion of the body?

Accepted Answer

The acceleration of every particle in the body is zero

Answer

The velocity of every particle in the body is constant

Answer

The kinetic energy of the body is constant

Answer

The angular momentum of the body is constant

Question 13

For a rigid body undergoing translational motion, which statement about its velocity and acceleration is accurate?

Accepted Answer

Velocity can be either constant or variable.

Answer

Acceleration is always constant.

Answer

Velocity is always variable.

Answer

Acceleration is always zero.

Question 14

Which of the following is considered a vector quantity?

Accepted Answer

Acceleration

Answer

Speed

Answer

Temperature

Answer

Mass

Question 15

If a rigid body is subjected to a constant torque, what is true about its rotational motion?

Accepted Answer

Its angular acceleration is constant.

Answer

Its angular velocity is constant.

Answer

Its angular displacement is constant.

Answer

Its angular momentum is constant.

Question 16

A rigid body undergoes pure translation. What is true about its angular acceleration?

Accepted Answer

Zero

Answer

Constant

Answer

Variable

Answer

Cannot be determined

Question 17

A particle moves along a curved path with a constant linear speed. What is the direction of its acceleration is directed?

Accepted Answer

Towards the center of curvature

Answer

Zero

Answer

Away from the center of curvature

Answer

Tangential to the path

Question 18

When a rigid body undergoes combined translation and rotation, which type of motion is not possible?

Accepted Answer

Rectilinear motion

Answer

Plane motion

Answer

Spherical motion

Answer

Cylindrical motion

Question 19

A rigid body experiences pure translational motion. Which statement accurately describes this scenario?

Accepted Answer

All particles of the rigid body have identical velocity and acceleration.

Answer

Velocities and accelerations of all particles are distinct.

Answer

Velocities of all particles are identical, while accelerations differ.

Answer

Accelerations of all particles are identical, while velocities differ.

Question 20

A wheel rotates about a fixed axis with constant angular velocity. Which statement about a particle on the rim of the wheel is incorrect?

Accepted Answer

It has constant tangential acceleration.

Answer

It maintains a constant tangential velocity.

Answer

It experiences constant radial acceleration.

Answer

It experiences constant centripetal acceleration.

Question 21

A rigid body undergoes general plane motion. What accurately describes its motion?

Accepted Answer

It exhibits both translational and rotational degrees of freedom.

Answer

It has only translational degrees of freedom.

Answer

It has only rotational degrees of freedom.

Answer

It lacks both translational and rotational degrees of freedom.

Question 22

The velocity of a rigid body can be determined using:

Accepted Answer

The velocity of any of its particles.

Answer

The angular velocity of the body.

Answer

The displacement of the body over time.

Answer

The acceleration of the body.

Question 23

A rigid body is in equilibrium when:

Accepted Answer

The net force acting on it is zero.

Answer

The net force acting on it is non-zero.

Answer

The force of gravity acting on it is zero.

Answer

The weight of the body is zero.

Question 24

When a rigid body is subjected to a torque, the resulting angular acceleration is:

Accepted Answer

Directly proportional to the applied torque.

Answer

Inversely proportional to the applied torque.

Answer

Independent of the applied torque.

Answer

Equal in magnitude to the applied torque.

Question 25

The work-energy principle for a rigid body undergoing plane motion can be expressed as:

Accepted Answer

W = T - U

Answer

W = U - T

Answer

W = T + U

Answer

W = 2T - U

Question 26

The impulse-momentum principle for a rigid body undergoing plane motion can be expressed as:

Accepted Answer

I = mv - mu

Answer

I = mu - mv

Answer

I = 2mv - mu

Answer

I = mv + mu

Question 27

Which of the following is NOT a kinematic variable?

Accepted Answer

Force

Answer

Displacement

Answer

Velocity

Answer

Acceleration

Question 28

A rigid body is translating at a constant velocity. Its acceleration is:

Accepted Answer

Zero

Answer

Constant

Answer

Variable

Answer

Cannot be determined

Question 29

Which of the following equations relates linear velocity and angular velocity for a point on a rotating body?

Accepted Answer

v = rω

Answer

v = ω/r

Answer

r = vω

Answer

ω = v/r

Question 30

A body is launched into the air with an initial velocity. Its trajectory is:

Accepted Answer

Parabolic

Answer

Linear

Answer

Circular

Answer

Hyperbolic

Question 31

Which of the following is a valid unit for angular velocity?

Accepted Answer

rad/s

Answer

m/s

Answer

m/s^2

Answer

rad/s^2

Question 32

A rigid body is subjected to a force F. The distance from the point of application of force to the axis of rotation is r. The moment of force (M) is given by:

Accepted Answer

M = F x r

Answer

M = F + r

Answer

M = F / r

Answer

M = r / F

Question 33

The velocity (v) of a rigid body rotating about a fixed axis with angular velocity (ω) is given by:

Accepted Answer

v = ω x r

Answer

v = ω + r

Answer

v = r / ω

Answer

v = ω – r

Question 34

The acceleration (a) of a rigid body rotating about a fixed axis with angular acceleration (α) is given by:

Accepted Answer

a = α x r

Answer

a = α + r

Answer

a = r / α

Answer

a = α – r

Question 35

A wheel rolls without slipping on a horizontal surface. The velocity of the center of the wheel (v) is related to its angular velocity (ω) and radius (r) as:

Accepted Answer

v = ωr

Answer

v = ωr^2

Answer

v = r / ω

Answer

v = ω / r

Question 36

The kinetic energy (T) of a rigid body rotating about a fixed axis is given by:

Accepted Answer

T = (1 / 2)Iω^2

Answer

T = (1 / 2)Iω

Answer

T = Iω^2

Answer

T = Iω

Question 37

The angular momentum (H) of a rigid body rotating about a fixed axis is given by:

Accepted Answer

H = Iω

Answer

H = Iω^2

Answer

H = (1 / 2)Iω

Answer

H = (1 / 2)Iω^2

Question 38

The work done (W) by a moment (M) acting on a rigid body through an angular displacement (θ) is given by:

Accepted Answer

W = Mθ

Answer

W = Mω

Answer

W = (1 / 2)Mθ^2

Answer

W = (1 / 2)Mω^2

Question 39

A rigid body is in equilibrium under the action of a number of forces. The necessary and sufficient condition for equilibrium is that:

Accepted Answer

Both the resultant force and moment acting on the body are zero

Answer

The resultant force acting on the body is zero

Answer

The resultant moment acting on the body is zero

Answer

Neither the resultant force nor the moment acting on the body is zero

Question 40

The velocity of a particle is defined as the:

Accepted Answer

Rate of change of position in a given direction

Answer

Rate of change of displacement

Answer

Rate of change of acceleration

Answer

Rate of change of velocity

Question 41

A particle moves along a straight line with a constant acceleration. Its initial velocity is 10 m/s and its acceleration is 5 m/s^2. What is its velocity after 5 seconds?

Accepted Answer

25 m/s

Answer

15 m/s

Answer

35 m/s

Answer

45 m/s

Question 42

Which of the following is the equation for the centripetal acceleration of a particle moving in a circular path?

Accepted Answer

a_c = v^2/r

Answer

a_c = v*r

Answer

a_c = r*v

Answer

a_c = 2πr/v

Question 43

A car moves around a circular track of radius 100 m with a speed of 20 m/s. What is its centripetal acceleration?

Accepted Answer

8 m/s^2

Answer

4 m/s^2

Answer

16 m/s^2

Answer

32 m/s^2

Question 44

A rigid body undergoes translational motion at a constant velocity. Which statement accurately describes its acceleration?

Accepted Answer

It is equal to zero.

Answer

It is constant but non-zero.

Answer

It varies with time.

Answer

Its value can't be determined without additional information.

Question 45

A rigid body exhibits pure rolling motion without slipping. Which statement about its motion is accurate?

Accepted Answer

Both linear velocity and angular velocity are constant.

Answer

Linear velocity is constant, while angular velocity changes with time.

Answer

Angular velocity is constant, while linear velocity changes with time.

Answer

Both linear velocity and angular velocity change with time.

Question 46

A flywheel possesses a moment of inertia I and rotates with an angular velocity ω. What is the flywheel's kinetic energy?

Accepted Answer

0.5Iω^2

Answer

Iω

Answer

0.5Iω

Answer

2Iω^2

Question 47

A rigid body undergoes plane motion. How are its velocity and acceleration typically oriented?

Accepted Answer

May be parallel, perpendicular, or neither

Answer

Always parallel

Answer

Always perpendicular

Answer

Always equal in magnitude

Question 48

A rigid body rotates about a fixed axis with constant angular acceleration. Which equation relates its angular displacement, angular velocity, and angular acceleration?

Accepted Answer

θ = ωt + 0.5αt^2

Answer

θ = ωt - 0.5αt^2

Answer

θ = ωt^2 + 0.5αt

Answer

θ = ωt^2 - 0.5αt

Question 49

For a particle moving in a circular path with constant speed, in which direction does its acceleration vector point?

Accepted Answer

Towards the center of the circle

Answer

Perpendicular to the velocity

Answer

Tangential to the circle

Answer

Zero

Question 50

A rigid body has an angular velocity of 10 rad/s about a fixed axis. What is its angular displacement after 5 seconds?

Accepted Answer

25 radians

Answer

50 radians

Answer

100 radians

Answer

200 radians

Question 51

A rigid body undergoes rotation about a fixed axis. Which of the following statements about its angular acceleration is true?

Accepted Answer

It can be positive or negative.

Answer

It is always zero.

Answer

It is always in the same direction as the angular velocity.

Answer

It is always tangential to the circle of rotation.

Question 52

A rigid body undergoes translational motion. What quantity remains constant throughout the motion?

Accepted Answer

Velocity

Answer

Acceleration

Answer

Angular velocity

Answer

Angular acceleration

Question 53

A rotating body has a constant angular velocity. What is the relationship between its linear velocity and angular velocity?

Accepted Answer

Linear velocity is directly proportional to angular velocity and the distance from the axis of rotation.

Answer

Linear velocity is inversely proportional to angular velocity and the distance from the axis of rotation.

Answer

Linear velocity is independent of angular velocity.

Answer

Linear velocity is equal to angular velocity.

Question 54

A wheel rolls without slipping. Which point on the wheel has zero velocity relative to the ground?

Accepted Answer

Point of contact with the ground

Answer

Topmost point

Answer

Lowest point

Answer

Center of the wheel

Question 55

Which of the following units is used to measure angular acceleration?

Accepted Answer

rad/s²

Answer

m/s

Answer

m/s²

Answer

rad/s

Question 56

For a rigid body undergoing translational motion with constant velocity, its acceleration is:

Accepted Answer

Zero

Answer

Non-zero and constant

Answer

Non-zero and variable

Answer

Dependent on the direction of motion

Question 57

A wheel rotating about its axis with a constant angular velocity is undergoing:

Accepted Answer

Pure rotation

Answer

Pure translation

Answer

Both translation and rotation

Answer

Neither translation nor rotation

Question 58

The acceleration of a point on a rigid body undergoing both translation and rotation is equal to:

Accepted Answer

The vector sum of translational and centripetal accelerations

Answer

The vector difference between translational and centripetal accelerations

Answer

Only the translational acceleration

Answer

Only the centripetal acceleration

Question 59

The path of a particle projected at an angle to the horizontal is:

Accepted Answer

A parabola

Answer

A straight line

Answer

A circle

Answer

An ellipse

Question 60

A rigid body undergoes pure translation. Which of the following statements regarding its angular velocity is **accurate**?

Accepted Answer

It is always zero.

Answer

It remains constant.

Answer

It varies with time.

Answer

It depends on the body's mass.

Question 61

A rigid body rotates about a fixed axis with **constant** angular acceleration. What is the relationship between its angular displacement and angular acceleration?

Accepted Answer

Quadratic

Answer

Linear

Answer

Exponential

Answer

Sinusoidal

Question 62

A projectile is launched with an initial velocity of V0 at an angle θ above the horizontal. What is the maximum height it will **attain**?

Accepted Answer

V0^2 sin^2 θ / 2g

Answer

V0^2 cos^2 θ / 2g

Answer

V0^2 / 2g

Answer

V0 / 2g

Question 63

A rigid body undergoes both translation and rotation. Which of the following statements about its linear and angular velocities is **correct**?

Accepted Answer

Both linear and angular velocities can vary.

Answer

Linear velocity is constant, while angular velocity can vary.

Answer

Angular velocity is constant, while linear velocity can vary.

Answer

Both linear and angular velocities are constant.

Question 64

A wheel rolls **without slipping**. What is the relationship between its linear and angular velocities?

Accepted Answer

v = rω

Answer

v = 2rω

Answer

v = rω/2

Answer

v = ω/r