# A Bicycle Momentum Problem...?

A bicycle has wheels of radius 0.29 m. Each wheel has a rotational inertia of 0.079 kgm2 about its axle. The total mass of the bicycle including the wheels and the rider is 78 kg. When coasting at constant speed, what fraction of the total kinetic energy of the bicycle (including rider) is the rotational kinetic energy of the wheels?

Relevance

K.E 1/2 m v^2 = 1/2 x 78 x v^2 = 39 v^2

R.K.E = 2[1/2 x moment of inertia x angular speed^2] as there are two wheels.

but as you know that v = r x angular speed

angular speed squared = v^2 / r^2

substituting this in the second equation we get

R.K.E = 2 x1/2 x 0.079 x v^2/0.29^2 = 0.9394 v^2

T.KE = KE + RKE = 39v^2 + 0.9394v^2

Now dividing 0.9394 v^2 with 39.9394 v^2 we get

0.0235 , the ratio required.

Hope my steps are clear enough...

• Find the rotational kinetic energy of the wheel and the translational kinetic energy of the bicycle. Add them together to find total kinetic energy. Simply find the ratio of rotational kinetic energy to total kinetic energy.

RKE/(RKE+TKE)

• Anonymous

Total K.E = translation KE + Rotation K.E of wheels

= 0.5*m*v^2 + Iw^2 + Iw^2

w = angular velocity

I = polar momemt of inertia of one wheel

Also w = v * r

Assuming there is no slipping of the tires, the horizontal velocity is same as the rotational velocity of the tires

So, the ratio = rotational K.E/ Total K.E

= (I*w*2/2 + I*w^2)/(I*w*2/2 + I*w^2 + 0.5*m*v^2)

= (I*v^2/r^2)/(I*v^2/r^2 + 0.5*mv^2)

= I/(I+0.5*m*r^2)

substituting values,