Question

Please show the work for how to get the answer. Thank you in advance.

Assume that all of the mass of a bicycle wheel is concentrated at its rim. Such a wheel of mass 1.2 kg and radius 30 cm starts from rest at the top of a hill 100 m long and inclined at 20� to the horizontal. What will be the speed of the wheel at the bottom of the hill if it rolls without slipping?
(Answer: 15 m/s)

Answer 1

since the exact shape of wheel is not given, so i'm considering wheel as a ring.so

I ( moment of interia) = m*r²                ( if it is in disc shape then I will be different so ans will be different)

by conservation of energy, energy at height h = energy at bottom

P.E = K.E ( translation) + K.E ( rotation)                           ( h= height of wheel = L*sin20)

mgh = (1/2)*m*V² + ( 1/2)*I*w²

mg ( L*sin 20) = ( 1/2)*m*V² + ( 1/2)*(m*r²) * ( V/r)²                               ( w = V/r)

V = ( g*L*sin 20)^1/2

V = 18.3 m/s

here ans in not exact match with your ans because exact shape of wheel is not given.put moment of interia accordingly the shape of wheel and then calculate V in similar manner as above.