Calculate the angular velocity of disc

A circular disc of mass 10 kg and radius 0.2 m is set in to rotation about an axis passing through its centre and perpendicular to its plane by applying torque 10 Nm. Calculate the angular velocity of disc that it will attain at the end of 6 sec from the rest.

Solution 

Given

Mass of the disc   =       m       =       10 kg

Radius of the disc =       r        =       0.2 m

Torque on disc      =       τ        =       10 Nm

Time                     =       s        =       6 sec

Angular velocity   =       ω       =       ?

at the end of 6 sec

The torque acting on rotating body can be given as

τ = I α

α = τ / α

where

α is angular acceleration

and

I is moment of inertia

As, the moment of inertia of disc rotating about an axis passing through its centre and  perpendicular to its plane is given by

I = M R² / 2

The angular acceleration becomes

α = 2 τ / M R²

Putting the values we get,

α = 2 X 10  / 10 X  ( 0.2 ) ²

α = 50 rad / sec

For a body rotating with initial angular velocity ω_o when accelerated with constant angular acceleration α then the final angular velocity of body can be given as

ω = ω_o + α t

ω = 0+ 50 X 6

ω = 300 rad/sec