A cart has two cylindrical wheels connected by a

weightless horizontal rod using weightless spokes and friction-

less axis as shown in the figure. Each of the wheels is made

of a homogeneous disc of radius R, and has a cylidrical hole

of radius R/2 drilled coaxially at the distance R/3 from the

centre of the wheel. The wheels are turned so that the holes

point towards each other, and the cart is put into motion on

a horizontal floor. What is the critical speed v by which the

wheels start jumping?

**My attempt:**

I have noticed that while rolling at constant speed, the centre of

mass of the whole cart moves also with a constant speed, i.e.

there should be no horizontal forces acting on the cart. Also,

each of the cylinders rotates with a constant angular speed,

hence there should be no torque acting on it, hence the friction force must be zero.

My book also gave a hint which I couldn't interpret-Use the rotating frame of a wheel;

Try to substitute one asymmetric body

(the cylinder with a hole) with two symmetric bodies, a hole-

less cylinder, and a superimposed cylinder of negative density.

Keep in mind that the rod can provide any horizontal

force, but cannot exert any vertical force.

The answer = $$v = {3\sqrt(g)\sqrt(R)}$$

Also, please would you read the instructions about loading images in the meta question http://physicsproblems.nfshost.com//?qa=253.

edited May 30, 2017 by sammy gerbil