Question

At a typical bowling alley the distance from the line where the ball is released (foul line) to the first pin is 18.29 m . Assume it takes 5.0 s for the ball to reach the pins after you release it if it rolls without slipping and has a constant translational speed. Also assume the mass of the ball is 5.44 kg and has a diameter of 21.6 cm .Calculate the rotation rate of the ball, in rev/srev/s.

Answer 1

To calculate the rotation rate of a bowling ball, divide its translational speed (found by distance over time) by the circumference of the ball. With the given parameters, the rotation rate is approximately 5.39 revolutions per second (rev/s).

Step-by-step explanation:

The question asks us to calculate the rotation rate of a bowling ball in revolutions per second (rev/s), given that it rolls without slipping for a distance of 18.29 meters in 5.0 seconds, has a mass of 5.44 kg, and a diameter of 21.6 cm. To find the rotation rate, we first need to calculate the translational speed of the ball. The translational speed v is the distance covered divided by the time taken, so:

v = d / t = 18.29 m / 5.0 s = 3.658 m/s

Next, we need to relate this speed to the rotation of the ball. The circumference C of the ball is given by C = π × diameter. With the diameter given as 0.216 m (21.6 cm), the circumference calculates to:

C = π × 0.216 m ≈ 0.6786 m

The rotation rate in rev/s is the translational speed divided by the circumference:

Rotation rate = v / C = 3.658 m/s / 0.6786 m ≈ 5.39 rev/s