Torque and Angular Momentum
Rotational analogue of force, conservation of angular momentum and equilibrium. (Physics › System of Particles and Rotational Motion, NEET UG syllabus.)
What is Torque and Angular Momentum?
The rotational analogue of force, representing the tendency of a force to cause rotation about an axis. It is a vector quantity.
Key formula / rule: Torque (vector form)
Key points
- Define torque and angular momentum and state their SI units.
- Calculate torque and angular momentum for particles and rigid bodies.
- Relate torque to the rate of change of angular momentum.
- State and apply the principle of conservation of angular momentum.
Common exam trap
Confusing scalar (dot) and vector (cross) products when calculating torque and angular momentum.
Definitions
- Term
Torque
- Meaning
The rotational analogue of force, representing the tendency of a force to cause rotation about an axis. It is a vector quantity.
- Term
Angular Momentum
- Meaning
The rotational analogue of linear momentum, representing the quantity of rotational motion an object possesses. It is a vector quantity.
- Term
Rotational Equilibrium
- Meaning
A state where the net external torque acting on a body is zero, resulting in no change in its angular velocity (either at rest or rotating with constant angular velocity).
Learning objectives
Define torque and angular momentum and state their SI units.
Calculate torque and angular momentum for particles and rigid bodies.
Relate torque to the rate of change of angular momentum.
State and apply the principle of conservation of angular momentum.
Understand the conditions for rotational equilibrium.
Solve problems involving rotational dynamics using these concepts.
Formulae
- Name
Torque (vector form)
- Note
r is position vector from axis to force application, F is force vector.
- Expression
τ = r × F
- Name
Magnitude of Torque
- Note
θ is the angle between r and F.
- Expression
τ = r F sinθ
- Name
Torque (rotational dynamics)
- Note
I is moment of inertia, α is angular acceleration.
- Expression
τ = Iα
- Name
Angular Momentum (particle, vector form)
- Note
r is position vector, p is linear momentum, m is mass, v is linear velocity.
- Expression
L = r × p = r × (mv)
- Name
Magnitude of Angular Momentum (particle)
- Note
θ is the angle between r and p (or v).
- Expression
L = r p sinθ = r m v sinθ
- Name
Angular Momentum (rigid body)
- Note
I is moment of inertia, ω is angular velocity.
- Expression
L = Iω
- Name
Relation between Torque and Angular Momentum
- Note
Net external torque equals rate of change of angular momentum.
- Expression
τnet = dL/dt
- Name
Conservation of Angular Momentum
- Note
Total angular momentum of a system remains constant if no net external torque acts on it.
- Expression
If τnet = 0, then L = constant (Linitial = Lfinal or I₁ω₁ = I₂ω₂)
Prerequisites
Vectors and vector cross product
Newton's Laws of Motion
Linear momentum
Rotational kinematics (angular displacement, velocity, acceleration)
Moment of Inertia
Common mistakes
Confusing scalar (dot) and vector (cross) products when calculating torque and angular momentum.
Incorrectly identifying the axis of rotation or the position vector 'r'.
Forgetting the vector nature of torque and angular momentum and only considering magnitudes.
Applying conservation of angular momentum when a net external torque is present.
Not using consistent units throughout calculations.
Misinterpreting the direction of torque or angular momentum.
Keywords
Torque
Angular Momentum
Moment of Force
Rotational Inertia
Conservation of Angular Momentum
Rotational Equilibrium
Cross Product
Right-Hand Rule
Moment of Inertia
Practice preview
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