A cart consists of a body and four wheels on frictionless axles. The body has a mass m. The wheels are uniform disks of mass M and radius R. The cart rolls, without slipping, back and forth on a horizontal plane under the influence of a spring attached to one end of the cart (figure). The spring constant is k. Taking into account the moment of inertia of the wheels, find a formula for the frequency of the back and forth motion of the cart.

Question

G1 Physics · Accepted Answer

For each solid-disk wheel rolling without slipping, rotational kinetic energy adds an effective mass I/R²=(1/2)M. Thus each wheel contributes M+(1/2)M=3M/2; four wheels contribute 6M. Total effective mass=m+6M, so ω=√[k/(m+6M)]. Correct answer: A.