A car travels at 90.6 km/h on a level road in the positive direction of an x axi

Question

A car travels at 90.6 km/h on a level road in the positive direction of an x axis. Each tire has a diameter of 70.2 cm. Relative to a woman riding in the car and in unit-vector notation, what are the velocity v Overscript right-arrow EndScripts 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 v Overscript right-arrow EndScripts 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

To find the velocity as seen from a frame of reference above the car, you have to subtract the velocity of this moving frame of reference:

velocity as seen from the car = velocity as seen from the ground - velocity of the car

(a) The center of the wheel moves at 90.6km/h , so the velocity relative to a woman inside the car is:

Vcenter,car = Vcenter,ground - Vcar,ground

where:

Vcenter,car : velocity of the center as seen from the car (relative to the woman inside the car)

Vcenter,ground : velocity of the center as seen from the ground

Vcar,ground : velocity of the car as seen from the ground

Vcenter,car = 90.6km/h - 90.6km/h

So the answer is:

Vcenter = 0

(b) First we need the velocity of the top as seen from the ground.

When the wheels are not slipping, the velocity of a point at the top is

Vtop = 2Vcenter

Then, to find the velocity relative to the woman inside the car:

Vtop,car = Vtop,ground - Vcar,ground

Vtop,car = 2*90.6km/h - 90.6km/h

Then the answer is:

Vtop = 90.6 km/h

(c) When the wheel is not slipping, the velocity for the point at the bottom (in contact with the ground) is zero.

Vbottom,car = Vbottom,ground - Vcar,ground

Vbottom,car = 0 - 90.6km/h

So the answer is

Vbottom = -90.6km/h

(d) The velocity of the center of the wheel is zero as seen from inside the car, and it's not changing. If the velocity does not change, there is no acceleration, so:

a(center) = 0

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Please submit the rest of the problem as a new question, there are too many subparts.

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