Question

A cat jumps onto a 400 kg ferris wheel with a radius of 5 m. The wheel is traveling at 4 rad/s. what is the angular velocity of the ferris wheel once the cat is on the edge? What is the angular velocity of the ferris wheel if the cat moves inward by 2 m?

Answer 1

if you have the mass of cat just plug it here to get the answer

i assume mass of cat = m_cat kg  

By angular momentum conservation / assuming car as a point mass

Li = Lf

Ii *wi = If *wf

m*r² *wi = ( m*r² +m_cat *r² )*wf

400*5^2*4 = (400*5^2 + m*5^2)*wf

wf = 40000 /(10000+25*m_cat) rad/s

if you have the mass of cat just plug it here to get the answer

if the cat moves inward by 2 m

Ii *wi = If *wf

m*r² *wi = ( m*r² +m_cat *d² )*wf

400*5^2*4 = (400*5^2 + m*3^2)*wf

wf = 40000 /(10000+9*m_cat) rad/s