Question

A spoked wheel with a radius of 44.0 cm and a mass of 1.90 kg is mounted horizontally on frictionless bearings. JiaJun puts his 0.550-kg guinea pig on the outer edge of the wheel. The guinea pig begins to run along the edge of the wheel with a speed of 18.0 cm/s with respect to the ground. What is the angular velocity of the wheel? Assume the spokes of the wheel have negligible mass.
rad/s

Honestly, I don't know how to calculate this, I have been trying to figure out but I have been guessing, and am sure they aren't write because they gave me wrong answers. Need help thank you in advance.

Answer 1

Since the bearings are frictionless, the total angular momentum of wheel and guinea pig remains zero, as they rotate in opposite directions.

0.18 m/s*0.550kg*0.44m
= 0.04356 kg m^2/s
= -Iwheel*w

The moment of inertia of the wheel is
Iwheel = M*R^2 = 1.90*(0.44)^2
= 0.3678 kg*m^2. Therefore
w = -0.118 rad/s

The minus sign indicates that it is turning in the opposite direction from the guinea pig.

Answer 2

Thank you so much; I really appreciate it!