A car travels at 80 km/h on a level road in the positive direction of an x axis. Each tire has a diameter of 66 cm. Relative to a woman riding in the car and in unit-vector notation, what are the velocity at the (a) center, (b) top, and (c) bottom of the tire and the magnitude a of the acceleration at the (d) center, (e) top, and (f) bottom of each tire? Relative to a hitchhiker sitting next to the road and in unit-vector notation, what are the velocity at the (g) center, (h) top, and (i) bottom of the tire and the magnitude a of the acceleration at the (j) center, (k) top, and (l) bottom of each tire?

80 km/h = 22.2 m/s

66 cm = 0.66 m

Relative to the woman riding in the car:

(a) Since the center of the tire is not moving, and the woman goes along with the movement of the car, v=0

(b) v = + 22.2 km/h, since the wheel turns at this velocity from left to right

(c) v = - 22.2 km/h, since the wheel turns at this velocity from right to left

(d) a = 0, since v=0

(e) a = v2/r = (+22.2) ^2 / (0.66 : 2) = 1493.45 m2/s

(f) a = v2/r = (-22.2) ^2 / (0.66 : 2) = - 1493.45 m2/s

Relative to hitchhiker:

(g) v = + 22.2 m/s, since from an external body, the velocity of the car is still observed

(h) v = + 22.2 x 2 = 44.4 m/s, since the top runs twice faster to be able to move the car

(i) v = 0, since from an external body, the bottom part of the tire is always in contact with the ground

(j) a = 0, because velocity is constant

(k) a = 1493.45 m2/s, same with that of the woman because both are inertial reference

(l) a = - 1493.45 m2/s, same with that of the woman because both are inertial reference