Answer:

A system rotating with an angular momentum in presence of a torque suffers a change in the angular momentum and the rate of change of angular momentum is directly proportional to the torque acting on it.

If I be the moment of inertia of the system and ω be the angular velocity then angular momentum L= Iω

Rate of change of angular momentum provided the shape of system does not change is :

τ= dt÷d = (Iω)=I×dω÷dt = Iα

α is the angular acceleration and τ is the torque.Dimension of Torque is [ML²T-2²] and its unit is Newton- metre (N⋅m).

Explanation:

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Q] Obtain the expression for the torque acting on a rotating(not relating)body with constant angular acceleration.

Solution:

Let's consider a rotating body having n number of particles at different radius.

Let their masses be and radius at which they are located be

Now, we know that Torque( ) = Force x radius

Calculating the torque of individual particle of the rotating body,we get:

Let's consider that the particles of the rotating body has their individual accelerations

Replace F by ma

Now, since the object is rotating, we will take into consideration, the tangential acceleration which is represented by where r is the radius and is the angular acceleration which is constant for all the particles of the body.

a=

Now,

Taking common, we get:

But, is moment of Inertia denoted by I

So, the final relation we get is