A circular metal disc of mass 200 g and radius 20 cm makes 10 revolutions per second about an axis passing through the centre and perpendicular to its plane. Find a) Moment of inertia about the axis, b) Torque required to change its angular velocity from 10 rps to 20 rps in 5 s.

A circular metal disc of mass 200 g and radius 20 cm makes 10 revoluti

1.	A circular metal disc of mass 200 g and radius 20 cm makes 10 revolutions per second about an axis passing through the centre and perpendicular to its plane. Find a) Moment of inertia about the axis, b) Torque required to change its angular velocity from 10 rps to 20 rps in 5 s.
Answer» Solution :Moment of inertia`I=(Mr^(2))/(2)=(200xx10^(-3)(20xx10^(-2)))/(2)=4xx10^(-3) kgm^(-2)` b)Torque `taualpha=(I(omega_(2)-omega_(1)))/(t) omega_(1)=2pin_(1)=2pixx10=20pi` `omega_(2)=2pin_(2)2pixx20=40pi,t=5 sectherefore TAU=(4xx10^(-3)(40 pi-20pi))/(5)` `=(4xx10^(-3)xx20pi)/(5)=16xxpixx10^(-3),tau=0.05 Nm`