Rotational Motion Mock Test for JEE Main 2025-26 Preparation

Translational motion means the whole body moves in the same direction and covers equal distances, whereas rotational motion means the body spins about an axis so different parts trace out circles of different radii. Key differences include:

• Translational: displacement is linear, defined by distance
• Rotational: displacement is angular, defined by angle (radians)
• Relevant quantities: force (translational) vs torque (rotational), mass vs moment of inertia

Moment of inertia (I) is a property of a body that quantifies its resistance to angular acceleration, much like mass in linear motion. The formula is I = Σ mᵢ rᵢ², where mᵢ is the mass of a particle and rᵢ its distance from the axis of rotation. It plays a central role when solving problems in rotational motion as it affects how a body responds to a given torque.

Angular velocity (ω) measures the rate of change of angular displacement, expressed in radians per second (rad/s). Angular acceleration (α) is the rate at which angular velocity changes, with the unit radians per second squared (rad/s²).

Newton's laws of rotational motion include:

• First law: A rotating object remains at rest or in uniform rotation unless acted upon by an external torque.
• Second law: Torque (τ) equals moment of inertia (I) times angular acceleration (α), or τ = Iα.
• Third law: For every torque exerted by one body on another, there is an equal and opposite torque.

Torque (τ) is the rotational analogue of force in linear motion. It measures how effectively a force causes an object to rotate about an axis. The magnitude is given by τ = r × F, where r is the position vector from the axis to the point of application and F is the force.

Conservation of angular momentum states that if no external torque acts on a system, its total angular momentum remains constant. This is crucial in problems like the spinning ice skater who spins faster when pulling in arms, as L = Iω remains constant if τ_ext = 0.

Rotational motion examples include:

• Spinning wheels (bicycle, car tires)
• Fans and propellers
• Earth's rotation about its axis
• Cycling pedals and merry-go-rounds
• Opening or closing a door around hinges

Mass measures how much matter an object has and its resistance to linear acceleration. Moment of inertia depends on both the distribution of mass relative to the rotation axis and the total mass, determining the object's resistance to rotational acceleration. While mass is scalar, moment of inertia depends on the axis chosen.

To solve rotational motion questions in JEE and MHT CET exams:

• Identify forces and torques acting on the object
• Calculate moment of inertia for the relevant axis
• Apply rotational equations of motion (e.g., θ = ω₀t + ½αt²)
• Use the conservation of angular momentum when no external torque acts
• Solve for required unknowns like angular velocity or kinetic energy

Uniform circular motion occurs when an object moves in a circle at constant speed. It is a special case of rotational motion where all points on the object travel with constant angular speed around the center. The acceleration experienced is called centripetal acceleration, which is always directed towards the center of the circle.

In rolling motion, an object (like a wheel) both rotates about its own axis and moves linearly along a surface without slipping. This combines rotational motion and translational motion. In pure rotational motion, only spinning occurs with no forward movement. For rolling without slipping, the velocity at the point of contact with the ground is zero relative to the surface.