Torque acting on rotating body

Hello dear we have know force is required to produce linear/ translational motion whose magnitude is given by, F = ma

In rotational motion, mass is replaced by moment of inertia and linear acceleration is replaced by angular acceleration so as to give rise the magnitude of force responsible for rotational motion.

According to definition torque or moment of force is the product of force and the moment arm hence torque is given as,

Let’s find the torque acting on rotating body……………!

Consider a rigid body consist ‘n’ number of particles having masses m1, m2…mn situated at distance r1, r2…rn respectively from the axis of rotation is rotating with uniform angular acceleration ‘a’. All particles are revolving with same angular acceleration but having different linear accelerations.

The linear acceleration of first particle is

∴ a1 = r1 α

Then by Newton’s 2nd law force acting on the particle is,

F1 = m1a1

But  a = r α

 

F1 = m1r1 α

τ = F1 x r1

τ_1 = m1r1 α  x r1

τ_1 = m1r12 α

Similarly,

τ_2  = m2r22α

 

τn  = mnrn2 α

Thus the total torque acting on the body is equal to sum of the torques acting on all the particles, given by,

Torque = M.I. x angular acceleration

This is the relation between M.I. & angular acceleration.

S.I. unit of torque is Nm and CGS unit is dyne cm

Dimensions of torque are [M1L2T-2]

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