Quiz on Rotational Dynamics

The moment of inertia of a body does not depend upon the________

• mass of the body

• position of the axis of rotation

• distribution of the mass

• the angular acceleration of the body

Answer explanation

The moment of inertia depends on the mass, position of the axis of rotation, and distribution of mass. However, it does not depend on the angular acceleration of the body, which relates to how the body rotates, not its inertia.

The SI unit of moment of inertia is________

• gram-cm²

• kg-m²

• kg/m²

• kg-m

Answer explanation

The moment of inertia is defined as the rotational equivalent of mass and is measured in kg-m² in the SI system. This unit reflects the mass distribution relative to the axis of rotation, making kg-m² the correct choice.

The dimensional formula for moment of inertia of a body is______

• L⁰M¹T-²

• L²M¹T⁰

• L¹M¹T-¹

• L⁰M²T-¹

Answer explanation

The moment of inertia (I) is defined as I = Σ(m * r²), where m is mass and r is the distance from the axis of rotation. Thus, its dimensional formula is L²M¹T⁰, indicating mass and distance squared.

The dimensional formula for the radius of gyration of a body is______

• L⁰M⁰T⁰

• L¹M⁰T⁰

• L¹M¹T⁰

• L⁰M²T-¹

Answer explanation

The radius of gyration (k) is defined as k = √(I/m), where I is the moment of inertia (L⁴M¹T⁻²) and m is mass (L⁰M¹T⁰). Thus, the dimensional formula for k simplifies to L¹M⁰T⁰, making L¹M⁰T⁰ the correct choice.

The SI unit of torque is_______

• N/m

• Nm²

• N-m

• N²m

Answer explanation

The SI unit of torque is Newton-meter, represented as N-m. This unit measures the rotational force applied at a distance, making N-m the correct choice among the options provided.

Which is the axial vector from the following?

• Linear Momentum

• Torque

• Velocity

• Acceleration

Answer explanation

Torque is an axial vector because it represents rotational force and has both magnitude and direction, specifically around an axis. In contrast, linear momentum, velocity, and acceleration are not axial vectors.

The rotational analogue of force is_________

• Moment of Inertia

• Angular Momentum

• Torque

• Angular Acceleration

Answer explanation

The rotational analogue of force is torque, which causes an object to rotate around an axis. Just as force causes linear acceleration, torque causes angular acceleration, making it the correct choice.

The physical quantity in translational motion, which analogous to torque in rotational motion is________

• Mass

• Linear Momentum

• Force

• Work

Answer explanation

In translational motion, force is the quantity that causes acceleration, similar to how torque causes angular acceleration in rotational motion. Thus, force is analogous to torque.

Torque per unit moment of inertia is________

• Radius of gyration

• Angular velocity

• Angular displacement

• Angular acceleration

Answer explanation

Torque per unit moment of inertia is defined as angular acceleration. This relationship shows how much angular acceleration is produced by a given torque, making 'angular acceleration' the correct answer.

The physical quantity in translational motion, which is analogous to moment of inertia in rotational motion is________

• Velocity

• Force

• Energy

• Mass

Answer explanation

In translational motion, mass is the quantity that determines how much an object resists acceleration, similar to how moment of inertia determines resistance to angular acceleration in rotational motion. Thus, the correct answer is mass.