You find yourself in your go-cart with ideal tires having coefficient of frictio

Question

You find yourself in your go-cart with ideal tires having coefficient of friction 1 on a turntable rotating at Omega. The cart is at a radius R from the center. Starting from the rest, you begin to drive in a circle of radius R about the center, accelerating with uniform acceleration a along the circular path. (The vectors are directed so that the radial component of the Coriolis force is outward.)

a) What is the condition on Omega, R and a for which you can begin to move without slipping?

b) Assuming that you can begin to move without slipping, how far can you travel before you do begin to slip?

Explanation / Answer

force on cart towards centre of circular path (centrifugal force) = m2R

acceleration towards centre of circular path direction = 2R

where m= mass, v= velocity in radial direction, R= radius

now as the cart started moving , it has an initial velocity of r

so net velocity in radial direction at a time t, v(t)=  r +

now acceleration in radial direction = a

a)

as cart has to be moved in circular path so the centrifugal force towards centre must be balanced with frictional force ie   

initially m2R = mg

or =sqrt(g/r)

b) now

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