Question

Derivation of torque acting on a rotating body. ​

Answer 1

Answer:

Explanation:

we know, angular momentum is the cross product of position of particle from the axis of rotation and linear momentum.

mathematically, if  denotes angular momentum,  denotes position of particle from axis of rotation and  denotes linear momentum.

then,  

we know,  

so,  

so, magnitude of angular momentum when angle between velocity and position of particle is 0°, L = mvr

we also know, rate of change of angular momentum per unit time is known as torque.

so,  

but  

so,  

or,  

or,  it is the expression for torque acting on rotating body with constant angular acceleration.