**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, I

_{1}ω_{1}= I_{2}ω_{2}**Example of conservation of Angular momentum**

- Motion of planets revolving in an elliptical orbit
- Diving into the swimming pool
- 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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