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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 .

torque

The angular momentum of this particle is;

Here Momentum vector p   is the linear momentum of the particle.fig angular momentum

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

L = rpsin90° = rp

Now p = mv    and     v = rω

Therefore, in terms of magnitudes,

ch5para5

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

 

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