A car travels at 81.9 km/h on a level road in the positive direction of an x axi

Question

A car travels at 81.9 km/h on a level road in the positive direction of an x axis. Each tire has a diameter of 69.2 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?

Explanation / Answer

a)velocity of the center w.r.t the car=0 velocity of the top=w*r=v=81.9 km/h in positive x direction velocity of the bottom=w*r=v=81.9 km/h in negative x diection b)acceleration of the center=0 accn of the top=v^2/r=747.92 m/s^2 downwards accen of the bottom=747.92 m/s^2 upwards c)velocity of the center w.r.t the ground=81.9km/h velocity of the top=w*r+v(c)=81.9 km/h+81.9 km/h=163.8 in positive x direction velocity of the bottom=w*r-v=0 d) acceleration of the center=v(c)^2/r=747.92 m/s^2 downwards accn of the top=v^2/r=2991.69 m/s^2 downwards accen of the bottom=0

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