A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of 
for 40 s, the speed increases to 2100 rpm. The diameter of the disk is _________m.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(40)
Mass of the disk, 
.
Initial angular velocity, 
.
Final angular velocity, 
.
External torque, 
.
Time, 
seconds.
First, convert the rotational speeds from revolutions per minute (rpm) to radians per second (rad/s):
Next, use the equation of motion for rotation to find the angular acceleration 
:
Solving for 
:
The torque and moment of inertia relationship is given by:
For a thin solid disk rotating along its diameter, the moment of inertia 
is 
. Thus:
Solving for 
:
The diameter of the disk is:
Diameter 
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