How does mass affect angular velocity?

1 Answer

Answer:

For a freely rotating rigid body

#omega\prop1/m#

Explanation:

For a freely rotating rigid body having mass #m#, radius of gyration #k# & an angular velocity #omega#, net torque #T_{\text{net}}# on the body must be zero

#T_{\text{net}}=0#

#I(\frac{d\omega}{dt})=0#

#\frac{d(I\omega)}{dt}=0#

#I\omega=\text{const}#

#mk^2\omega=\text{const}#

#\omega=\frac{\text{const}}{mk^2}#

#omega\prop1/m#

thus when the mass #m# of a freely rotating rigid body increases its angular velocity #\omega# decreases & vice-versa