Angular Acceleration of a Car's Wheel Calculation

How can we calculate the angular acceleration of a car's wheel and the number of revolutions turned by a wheel during acceleration?

Given a car accelerates uniformly from rest to a speed of 15 m/s in a time of 20s with a radius of 1/3 m.

Calculating Angular Acceleration and Number of Revolutions

Based on the data provided, the angular acceleration of the car's wheel can be found using the equation w = v/r, where: - w is the angular velocity, - v is the linear velocity, and - r is the radius of the wheel.

Then, to determine the number of revolutions turned by a wheel, we can use the formula N = w/2π, where: - N is the number of revolutions, and - w is the angular velocity.

To calculate the angular acceleration of the car's wheel, we can substitute the given values into the equation:

w = v/r

Angular velocity w = 15 m/s / (1/3 m) = 45 rad/s

Therefore, the angular acceleration of the car's wheel is 45 rad/s.

To find the number of revolutions turned by the wheel, we can apply the formula:

N = 45 rad/s / (2π) ≈ 7.16 revolutions

Hence, the wheel completes approximately 7.16 revolutions during the acceleration process.