Physics of bowling
This week I went to a bowling alley in Philadelphia and thought about physics and rotational motion while playing. I noticed that the a bowling lane is about 18 meters long and a 15-pound (6.8 kg) ball rolled for about 6 seconds before hitting the pins. The radius of a standardized 15-pound bowling ball is 8.5’’ (0.22 m)
=> v(ball) = 18/6 = 3 m/s
=> w(ball) = v/r = 3/0.22 = 13.6 rad/s = (13.6 *60)/(2π) = 130 rpm
For the sake of simplicity, I assumed that the ball accelerated very briefly before entering the 18-meter lane, and throughout the 18-meter lane, it travelled at constant rotational speed.
=> a(tan) = rα = 0
a(radial) = a(linear) = w2r = 13.62 * 0.22 = 40.7 m/s2
=> F = m*a(linear) = 6.8 * 40.7 = 276.7 N