ROTATIONAL DYNAMICS

Question 1

What is rotational dynamics?

Answer 1

The study of the motion of objects that rotate about an axis.

Question 2

What is the moment of inertia?

Answer 2

A measure of an object’s resistance to changes in its rotation.

Question 3

True or False: Torque is the rotational equivalent of force.

Answer 3

True

Question 4

Fill in the blank: The formula for torque (τ) is τ = ____ × r × sin(θ).

Answer 4

F

Question 5

What is the relationship between angular velocity and linear velocity?

Answer 5

Linear velocity (v) is equal to angular velocity (ω) multiplied by the radius (r): v = ω × r.

Question 6

Define angular acceleration.

Answer 6

The rate of change of angular velocity.

Question 7

What is the unit of torque?

Answer 7

Newton-meter (Nm).

Question 8

True or False: The moment of inertia depends on the mass distribution relative to the axis of rotation.

Answer 8

True

Question 9

What is the formula for calculating the moment of inertia of a solid cylinder about its central axis?

Answer 9

I = (1/2) m r², where m is the mass and r is the radius.

Question 10

Multiple Choice: Which of the following has the largest moment of inertia? A) Point mass B) Solid sphere C) Hollow sphere D) Solid cylinder

Answer 10

C) Hollow sphere

Question 11

What is the principle of conservation of angular momentum?

Answer 11

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

Question 12

Fill in the blank: The rotational kinetic energy (K) is given by K = ____ × I × ω².

Answer 12

1/2

Question 13

What does the term ‘gyroscope’ refer to?

Answer 13

A device that uses the principles of angular momentum to maintain orientation.

Question 14

What is precession in rotational dynamics?

Answer 14

The process by which the axis of a spinning object moves in response to an applied torque.

Question 15

True or False: A heavier object always has a greater moment of inertia.

Answer 15

False

Question 16

What is the relationship between torque and angular acceleration?

Answer 16

Torque is equal to the moment of inertia multiplied by angular acceleration: τ = Iα.

Question 17

Define centripetal force in the context of circular motion.

Answer 17

The net force directed towards the center of the circular path that keeps an object moving in a circle.

Question 18

Multiple Choice: Which quantity is conserved in the absence of external torques? A) Linear momentum B) Angular momentum C) Energy D) All of the above

Answer 18

B) Angular momentum

Question 19

What is the effect of increasing the radius on the moment of inertia?

Answer 19

Increasing the radius increases the moment of inertia.

Question 20

Fill in the blank: The angular momentum (L) is given by L = ____ × I × ω.

Answer 20

m

Question 21

What is the significance of the parallel axis theorem?

Answer 21

It allows the calculation of the moment of inertia about any axis parallel to an axis through the center of mass.

Question 22

What is the formula for the moment of inertia of a thin rod about its end?

Answer 22

I = (1/3) m L², where m is the mass and L is the length.

Question 23

True or False: The angular displacement is a scalar quantity.

Answer 23

False

Question 24

What is rotational equilibrium?

Answer 24

A state where the sum of all torques acting on an object is zero.

Question 25

What is the unit of angular velocity?

Answer 25

Radians per second (rad/s).

Question 26

Define the term 'radius of gyration'.

Answer 26

The distance from the axis of rotation at which the total mass of the body can be thought to be concentrated for the purpose of calculating the moment of inertia.

Question 28

Derive an expression for maximum speed of a vehicle moving along a horizontal circular track.

Answer 28

To derive an expression for the maximum speed of a object moving along a horizontal circular track without slipping, we consider the balance between the centripetal force needed for circular motion and the maximum static friction force which prevents slipping .