Final answer:
The angular velocity of a tire is calculated using the car's linear velocity and tire radius, and is expressed in radians per second or revolutions per minute. The centripetal acceleration is found using the square of the angular velocity and the tire radius. To count the number of revolutions before coming to rest, angular kinematics equations are needed, taking into account the initial angular velocity and time to stop.
Step-by-step explanation:
Angular Velocity of Rotating Tires
To calculate the angular velocity of car tires, you can use the formula ω = v / r, where ω is the angular velocity in radians per second, v is the linear velocity of the car, and r is the radius of the tire. For example, with a tire radius of 0.300 meters and a car velocity of 15.0 meters per second, the tire's angular velocity is (15.0 m/s) / (0.300 m) = 50.0 rad/s. To convert this to revolutions per minute (rev/min), you divide by 2π to get revolutions per second, and then multiply by 60 seconds per minute.
The centripetal acceleration at the edge of the tire can be calculated with the formula a = (v^2) / r, where a is the centripetal acceleration, and v is the linear velocity at the edge of the tire. Since the linear velocity is the product of angular velocity and radius (v = ω×r), we can rewrite the formula as a = (ω^2×r). Plugging in the angular velocity and tire radius into this formula will give us the centripetal acceleration.
For calculating the number of revolutions a tire makes before coming to rest given an initial angular velocity, we can use the concepts of angular kinematics. Assuming constant angular deceleration, the number of revolutions is found using the relationship between angular displacement, initial angular velocity, angular acceleration, and the time it takes to come to rest. This involves using kinematic equations adapted for rotational motion.