Master Rotational Motion: Enhance Your Physics Skills

Question 1

The angular momentum of a particle moving in a circle of radius r with linear velocity v is:

Accepted Answer

mvr

Answer

2mvr

Answer

mr^2 v

Answer

2mr^2 v

Question 2

A particle moves in a circular path of radius 'r'. Its centripetal acceleration is given by:

Accepted Answer

v²/r

Answer

r²/v

Answer

v/r

Answer

r/v

Question 3

Which of the following is a unit of torque?

Accepted Answer

Newton-meter (N⋅m)

Answer

Kilogram-meter (kg⋅m)

Answer

Joule (J)

Answer

Watt (W)

Question 4

Define the law of conservation of angular momentum and provide real-world examples that demonstrate its application.

Accepted Answer

The total angular momentum of a closed system remains constant.

Answer

Angular momentum can be freely created or destroyed.

Answer

The law of conservation of angular momentum only applies to systems with constant angular velocity.

Answer

The law of conservation of angular momentum is not a fundamental principle in physics.

Question 5

An object rotates in a vertical plane about a fixed horizontal axis. Which statement best describes the angular momentum of the object about the axis?

Accepted Answer

It is conserved if no external torque acts on the object.

Answer

It is proportional to the object's rotational kinetic energy.

Answer

It is zero if the object's center of mass is on the axis of rotation.

Answer

It is always in the same direction as the object's angular velocity.

Question 6

Which of the following has the greatest moment of inertia about its center of mass?

Accepted Answer

A solid sphere of radius R

Answer

A thin spherical shell of radius R

Answer

A hoop of radius R

Answer

A point mass at a distance R from the axis of rotation

Question 7

Which of the following is an effect of a spinning object's resistance to changes in its axis of rotation?

Accepted Answer

Gyroscopic effect

Answer

Centripetal effect

Answer

Centrifugal effect

Answer

Coriolis effect

Question 8

A particle of mass 'm' is moving in a circular path of radius 'r' with constant speed 'v'. Calculate its centripetal force.

Accepted Answer

mv²/r

Answer

½mv²r

Answer

4mv²/r

Answer

2mv²r

Question 9

A particle is moving in a horizontal circle with constant speed. What is the direction of its acceleration?

Accepted Answer

Towards the center of the circle

Answer

Zero

Answer

Away from the center of the circle

Answer

Tangential to the circle

Question 10

A uniform rod of mass m and length L pivots about an axis perpendicular to its length and passing through its center of mass. What is its moment of inertia about this axis?

Accepted Answer

(1/12) * m * L^2

Answer

(1/4) * m * L^2

Answer

(1/3) * m * L^2

Answer

(1/6) * m * L^2

Question 11

A flywheel of radius R and mass M is rotating with constant angular speed about a fixed axis through its center. What is its angular momentum?

Accepted Answer

1/2 * M * R^2 * ω

Answer

1/4 * M * R^2 * ω

Answer

1/8 * M * R^2 * ω

Answer

1/16 * M * R^2 * ω

Question 12

A small particle moves in a circular path of radius r with constant speed v. What is its centripetal acceleration?

Accepted Answer

v^2 / r

Answer

v^2 / 2r

Answer

v^2 / 4r

Answer

2 * v^2 / r

Question 13

A torque of τ is applied to a rigid body of moment of inertia I. What is the resulting angular acceleration?

Accepted Answer

τ / I

Answer

τ * I

Answer

I / τ

Answer

I * τ

Question 14

A particle is traveling in a circle of radius r with angular speed ω. What is its tangential speed?

Accepted Answer

r * ω

Answer

ω^2 * r

Answer

r / ω

Answer

ω / r

Question 15

A torque of τ is applied to a rigid body of moment of inertia I. What is the power required to maintain this torque?

Accepted Answer

τ * ω

Answer

ω / τ

Answer

τ / ω

Question 16

A particle of mass m moves in a circular path of radius r with uniform speed v. The magnitude of its angular momentum is:

Accepted Answer

mvr

Answer

mr²v

Answer

2mrv

Answer

0

Question 17

A flywheel of moment of inertia I is rotating with angular velocity ω. The work done in bringing it to rest is:

Accepted Answer

1/2 Iω²

Answer

0

Answer

Iω²

Answer

1/4 Iω²

Question 18

A uniform rod of length L and mass M is pivoted at one end. The moment of inertia of the rod about the pivot is:

Accepted Answer

1/3 ML²

Answer

ML²

Answer

1/2 ML²

Answer

1/4 ML²

Question 19

A uniform disc of mass M and radius R is rotating with an angular velocity ω. The angular momentum of the disc is:

Accepted Answer

1/2 MR²ω

Answer

2MR²ω

Answer

MR²ω

Answer

1/4 MR²ω

Question 20

A solid cylinder of radius R and height h rolls without slipping down an inclined plane of height H. The velocity of the cylinder at the bottom of the plane is:

Accepted Answer

√(2gH)

Answer

0

Answer

2√(gH)

Answer

√(gH)

Question 21

A particle of mass m is attached to a string of length L and is whirled in a vertical circle. The tension in the string at the top of the circle is:

Accepted Answer

mg + mv²/L

Answer

mg - mv²/L

Answer

2mg + mv²/L

Answer

mg

Question 22

A hoop of mass M and radius R is rolling without slipping on a horizontal surface. The kinetic energy of the hoop is:

Accepted Answer

1/2 MR²ω²

Answer

1/4 MR²ω²

Answer

MR²ω²

Answer

0