If the points of the car wheel move with an acceleration of 0.9 km / s ^ 2

If the points of the car wheel move with an acceleration of 0.9 km / s ^ 2 and the wheel radius is 45 cm, then the wheel rotation frequency is equal to.

Given:

a = 0.9 km / s2 = 900 m / s2 – centripetal acceleration of points of the car wheel;

R = 45 centimeters = 0.45 meters – the radius of the car wheel.

It is required to determine u (Hertz) – the wheel speed of the car.

Let’s find the linear speed of the points of the car wheel:

v = (a * R) ^ 0.5 = (900 * 0.45) ^ 0.5 = 405 ^ 0.5 = 20.1 meters per second.

Then the wheel speed of the car will be equal to:

v = 2 * pi * R * u, hence:

u = v / (2 * pi * R) = 20.1 / (2 * 3.14 * 0.45) = 20.1 / 2.8 = 7.2 Hertz.

Answer: The wheel speed is 7.2 Hertz.