1. Introduction
Rotational motion is a type of motion where a body rotates about an axis. It's a fundamental
concept in physics, extending the principles of linear motion to rotating systems. It's an
essential topic for JEE as it connects mechanics with other areas like thermodynamics and
gravitation.
2. Key Concepts
• Rigid Body: A rigid body is an idealization of a solid body in which deformation is
neglected. In other words, the distance between any two given points of a rigid body
remains constant in time.
• Axis of Rotation: The axis of rotation is the imaginary line about which a body
rotates. It can be fixed or it can move.
• Moment of Inertia (I): This is the rotational analog of mass. It's a measure of an
object's resistance to a change in its rotational motion.
o For a system of particles: I=∑miri2
o For a continuous body: I=∫r2dm
o Units: kg⋅m2
3. Torque (τ)
Torque is the rotational analog of force. It's a measure of how much a force acting on an
object causes that object to rotate.
• τ=r×F
• Magnitude: τ=rFsinθ
• Units: N⋅m
• Relation to angular acceleration: τnet=Iα
4. Angular Momentum (L)
Angular momentum is the rotational analog of linear momentum (p=mv).
• For a particle: L=r×p=r×(mv)
• For a rigid body: L=Iω
• Units: kg⋅m2/s
• Law of Conservation of Angular Momentum: If the net external torque on a system
is zero, the total angular momentum of the system remains constant. τext=dtdL
=0⇒L=constant
5. Rotational Kinetic Energy (KER)
• KER=21Iω2
• Total kinetic energy of a body undergoing both translational and rotational motion is
KEtotal=21mvCM2+21ICMω2
6. Parallel Axis Theorem & Perpendicular Axis Theorem
These theorems are very useful for calculating the moment of inertia of complex shapes.
Rotational motion is a type of motion where a body rotates about an axis. It's a fundamental
concept in physics, extending the principles of linear motion to rotating systems. It's an
essential topic for JEE as it connects mechanics with other areas like thermodynamics and
gravitation.
2. Key Concepts
• Rigid Body: A rigid body is an idealization of a solid body in which deformation is
neglected. In other words, the distance between any two given points of a rigid body
remains constant in time.
• Axis of Rotation: The axis of rotation is the imaginary line about which a body
rotates. It can be fixed or it can move.
• Moment of Inertia (I): This is the rotational analog of mass. It's a measure of an
object's resistance to a change in its rotational motion.
o For a system of particles: I=∑miri2
o For a continuous body: I=∫r2dm
o Units: kg⋅m2
3. Torque (τ)
Torque is the rotational analog of force. It's a measure of how much a force acting on an
object causes that object to rotate.
• τ=r×F
• Magnitude: τ=rFsinθ
• Units: N⋅m
• Relation to angular acceleration: τnet=Iα
4. Angular Momentum (L)
Angular momentum is the rotational analog of linear momentum (p=mv).
• For a particle: L=r×p=r×(mv)
• For a rigid body: L=Iω
• Units: kg⋅m2/s
• Law of Conservation of Angular Momentum: If the net external torque on a system
is zero, the total angular momentum of the system remains constant. τext=dtdL
=0⇒L=constant
5. Rotational Kinetic Energy (KER)
• KER=21Iω2
• Total kinetic energy of a body undergoing both translational and rotational motion is
KEtotal=21mvCM2+21ICMω2
6. Parallel Axis Theorem & Perpendicular Axis Theorem
These theorems are very useful for calculating the moment of inertia of complex shapes.
