You and your friends plan to roll down a hill on the inside of 600-pound tractor tire (diameter D = 1.80 m). The hill is inclined at an angle of 25.0° and you initially plan to start from a distance L = 100 m up the hill, but decide to first check whether it will be safe.

(a) Assuming the masses of the tire and your 105-pound body are concentrated at the outer rim of a thin-walled cylinder/hoop, what is the effective acceleration your body experiences at the bottom of the hill where your angular speed is greatest, i.e., how many “g’s” will you experience? Assuming the human body can withstand a g force of 8.00 g’s (1 g = 9.80 m/s²), is it safe to make the ride from 100 m up the hill?

(b) What is the maximum starting distance (L_max) up the hill that is safe?