Deduce the relation between tarque and angular momentum

1.	Deduce the relation between tarque and angular momentum
Answer» Angular momentum(L):- It is an measure of the rotation of body, taking into account its mass , shape and speed.\xa0L = r ×\u200b pwhere r is distance from the axis of rotation and the p is the linear momntum of the body.Torque(τ): It is an moment of force i.e. tendency of a force to rotate an object about an axis.We have shown that Newton\'s second law can be written asΣF\xa0=\xa0dp/dt.where ΣF\xa0is the net force acting on a body. Thus we can writer\xa0´\xa0ΣF\xa0=\xa0r\xa0´\xa0dp/dt.Since the net torque acting on a body is Στ =\xa0r\xa0´\xa0ΣF, and since we can add to the right hand side of the preceding equation the quantity\xa0dr/dt\xa0´\xa0p\xa0= 0 without changing its value, we can writeΣτ =\xa0r\xa0´\xa0dp/dt + dr/dt\xa0´\xa0p =\xa0d(r\xa0´\xa0p)/dt.We define angular momentum as\xa0L\xa0º\xa0r\xa0´\xa0pThe preceding equation then becomesΣτ\xa0=\xa0d\xa0L/dt,which is the rotational analogue of Newton\'s second law as expressed at the top of this derivation. (We note that\xa0like torque, which depends both upon the net force applied to a body and the point about which that torque is\xa0calculated, a body\'s angular momentum depends upon the net momentum of the body and upon the point about\xa0which its angular momentum is calculated.)

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