# Principle of Conservation of Angular Momentum | Physics Grade XI

### Conservation of Angular Momentum

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#### Kinematics

Introduction to Kinematics

# Principle of Conservation of Angular Momentum

Relationship between Angular Momentum and Torque
The angular momentum of the body is given by, L = I. ω ……. (i)

Differentiating equation (i) w.r.t time,
dL/dt = d/dt (I. ω)
dL/ dt = I dω/ dt
dL/ dt = Iα
Since we know τ = Iα, we can say
τ = dL/ dt

Hence, we can say that torque acting on a body is equal to the time rate of change of angular momentum.

Principle of conservation of Angular Momentum
It states that if no torque acts on the system the angular momentum remains unchanged.
According to definition, I. ω = constant

Proof:
We know, torque acting on a body is equal to time rate of change of angular momentum of the system about the axis of rotation,
τ = dL/ dt
since no torque acts on the system,
dL/ dt = 0
L = constant
.: I. ω = constant, which is the Principle of conservation of angular momentum
In general, I1 ω1 = I2ω2

Example of conservation of Angular momentum

1. Motion of planets revolving in an elliptical orbit
2. Diving into the swimming pool
3. Ballet dancer while spinning fold his/her hands to spin fast and extends his/her hands to slow the spin rate

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