Angular acceration of wheels???

Question

Okay I need to know what the Angular Acceration of the wheels of a car that is traveling at a constant speed of 36km/h along curved road of radius R = 100m. Please help!!!! and if you could include the formula plz

Diameter of the wheels d=1m

Answer 1

This is a good question, and one that I was thinking about just recently.

Let ω be the angular velocity of the wheel = v/(d/2)
= 10m/s / 0.5m = 20 rad/s

The magnitude of this is constant since the car has constant speed, however the direction of hte axis of rotation changes.

Unfortunately I can't draw a diagram here,
but dω/dt = ω * v/R
= 20 * 10 / 100
= 2 rad/s^2

Answer 2

This is a situation similar to gyroscopic precession. The angular momentum of the spinning wheels is being rotated by the constraint of the curved track at a rate w2 = (36000/3600)/R. You could compute the wheel angular momentum H = I * w1 (where w1 = (36000/3600)/(d/2)) if you know the moment of inertia I of the wheel. Then I * alpha = dH / dt. (See ref.) But I can be divided out and you get alpha = dw1 / dt = w2 * w1. Alpha is about a vertical axis.

Answer 3

There is no angular acceleration of the wheels. If the car travels at the same speed, the wheels rotate at the same speed.

Answer 4

angular acceleration is v^2/r

You would have to convert 36km/h to m/s, square it, and then divide by the radius of the road