**Question 2: Show that angular momentum in magnitude is given by**

ANSWER

Torque produces or changes the rotation of a particle about an axis of rotation. This means torque produces angular acceleration α.

Torque is defined as the twisting (turning) force that tends to cause rotation.

*Angular momentum is the quantity of motion of a body that is moving in a circle. Quantity of motion means how easy or difficult it is to stop the body from moving in the circle.* |

Physically, it is the cross product of moment arm and force .

The angular momentum of this particle is;

Here is the linear momentum of the particle.

Consider a body in motion in a circular path as shown in the figure. is perpendicular to at any point of the circular path. Therefore, momentum is tangential to the circle. The angle between and is 90° and hence,

L = rpsin90° = rp

Now p = mv and v = rω

Therefore, in terms of magnitudes,

Equations (Y) and (Z) prove the result.

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