Final answer:
The question asks to calculate the constant angular acceleration and the number of revolutions for a wheel slowing down to a stop. The strategy involves converting linear velocity to angular velocity, using kinematic equations, and then determining the revolutions by dividing the angular distance by 2π.
Step-by-step explanation:
The subject of this question is calculating the constant angular acceleration of a wheel and the number of revolutions it makes before coming to rest. The given problem involves a wheel of 50 inches in diameter, with an initial speed of 60 mph, which comes to rest after traveling a linear distance of 600ft. To solve for the angular acceleration, we need to use kinematic equations that link angular motion to linear motion, and then apply them to determine the number of revolutions the wheel makes before stopping.
Strategy to Solve the Problem:
Convert the initial linear velocity to angular velocity in radians per second (rad/s).
Use the kinematic equation v2 = u2 + 2as, where v is the final velocity (0 rad/s), u is the initial velocity (in rad/s), a is the angular acceleration, and s is the distance (converted to radians).
Calculate the number of revolutions by dividing the angular distance by 2π (since 2π radians equate to one revolution).
To help understand the concepts, students can refer to similar examples such as the braking of a bicycle wheel or the acceleration of train wheels, as these provide scenarios with designated angular accelerations similar to the one asked in the question.