Question

A wheel of moment of inertia 0.5 kg m2 and radius 20 cm is rotating about its axis at an angular speed of 20 rad/s. It picks up a stationary particle of mass 200 g at its edge. Find the new angular speed of the wheel.

Answer 1

Answer:

$\omega_{f}=19.685\ rad/s$  

Explanation:

given,  

radius of the wheel = 20 cm

moment of inertia of wheel = 0.5 kg m²

mass  = 200 g = 0.2 kg

angular speed of the wheel = 20 rad/s

initial angular momentum of the system  

$L_i = I\omega_i$  

$L_i = 0.5 \times 20$  

$L_i =10\ kgm^2/s$  

final angular momentum of the system  

$L_f = (I_{disk}+mR^2)\omega_{f}$  

$L_f = (0.5 + 0.2\times 0.2^2)\omega_{f}$  

$L_f= (.508)\omega_{f}$  

from conservation of angular momentum  

$L_i = L_f$  

$10 = (.508)\omega_{f}$  

$\omega_{f}=19.685\ rad/s$