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