How fast is the car moving when

[sona1177]

A 1.2 g pebble is stuck in a tread of a .76 -m-diameter automobile tire, held in place by static friction that can be at most 3.6 N. The car starts from rest and gradually accelerates on a straight rode . How fast is the car moving when the pebble flies out of the tire tread?

Alpha= net Torque/moment of Inertia

So net torque is 3.6 * .38= 1.368 N-m. Moment of inertia is .5mr^2 so that's .5 * .0012 * .38 ^2= 8.664 * 10^-5. so 1.368 N-m/ (8.664 kg-m^2)= 15789 rad/s^2. Now I need to find Theta and then use wf^2= wi^2 + 2alpha * theta. Then use v=wr. But how do I find theta when I don't know the distance is has traveled around the circle. Is it 2pi*r? I am having trouble because how do I know how Many times this pebble went around the circle? I can't find theta if I don't know the full distance is traveled around the circle since theta= s/r where s is the distance the particle goes on it's circular path. How do I find theta?

 

[rl.bhat]

As long as the frictional force is greater than the centripetal force on the pebble, the pebble will stay in the tire thread. When the centripetal force is greater than the frictional force, the pebble will fly off.