Physics rotation?

Question

A car traveling on a flat (unbanked) circular track accelerates uniformly from rest with a tangential acceleration of 2.10 m/s^2. The car makes it .25 of the way around the circle before it skids off the track. What is the coefficient of static friction between the car and track?

The tires of a 1475 kg car are 0.591 m in diameter and the coefficients of friction with the road surface are µs = 0.8 and µk = 0.6. Assuming that the weight is evenly distributed on the four wheels, whats the maximum torque that can be exerted by the engine on driving wheel such that the wheel does not spin. Suppose that the car is at rest.

A bus is designed to draw its power from a rotating flywheel that is brought up to its maximum rate of rotation (3060 rev/min) by an electric motor. The flywheel is a solid cylinder with a mass of 1100 kg and diameter 1.03 m. If the bus requires an average power of 9.1 kW, how long does the flywheel rotate?

Can someone help me on at least one of them?

Answer 1

I'll take the 3rd question.
Cylinder moment of inertia I = mr^2/2
Kinetic energy KE = Iω^2/2
ω = 3060/60*2pi
Time t = KE/P

Actually the 1st question looks interesting because there doesn't seem to be enough info. Let's give it a hack.
Given a = 2.1 m/s^2; θ = pi/2
s = at^/2 = v^2/(2a) ==> v^2 = 2as = 2aθr
At slip, Ff = Fc ==> μmg = mv^2/r
μ = v^2/(r*g) = 2aθ/g
μ = 0.6732

Well, now there's only one left and it's easy. I assume "on driving wheel" means on 1 not all drive wheels. If not multiply the answer by the number of drive wheels.
Ff = 0.25µmg
r = 0.591/2
T = r*F
To not spin, µs should be used for µ.

Answer 2

G = 6.7*10^(-11) M = 5.97*10^24..........the mass of earth T = 2 * pi * ( r^3 / (G*M) )^(1/2) = 86400 so the answer is r = 4.23*10^7 m