Roberto is with some friends at a local bowling alley. Roberto has some inside information from the manager, over the first two-thirds of the lane, the coefficient of kinetic friction between the rental balls and the lane surface is 0.190 (near the pins, the coefficient will be larger). The rental balls come in a wide variety of weights, Roberto has selected a ball which weighs 59.0 N. The radius of a tenpin bowling ball is 10.80 cm. Note: bowling balls generally do NOT have a uniform mass distribution, you should not assume that Roberto's ball does have a uniform distribution of mass. Roberto is a novice bowler and releases the ball with very little spin. He notices that, once the ball leaves his hand, it always begins its trip toward the pins by slipping (or sliding) along the surface of the lane; and, as it slides, the spin rate is gradually increasing. At some point along the lane, the spin rate exactly correlates with the speed of the ball and the ball begins to roll without slipping. Roberto notices that, for his throws, rolling without slipping always begins at about the same location along the lane. Stepping off the distance, he finds that the distance from his release point to the "rolling-without-slipping point is about 5.639 m (the distance from the foul line to the head pin is 18.29 m). Eager to estimate his release speed, he asks his friend Sharon to measure the time between release and rolling-without-slipping. Sharon takes measurements of the time interval for several of Roberto's throws, and arrives at an average of 1.015 seconds. At this particular bowling alley, the pins are due West of the bowlers.

Roberto is with some friends at a local bowling alley. Roberto has some inside information from the manager, over the first two-thirds of the lane, the coefficient of kinetic friction between the rental balls and the lane surface is 0.190 (near the pins, the coefficient will be larger). The rental balls come in a wide variety of weights, Roberto has selected a ball which weighs 59.0 N. The radius of a tenpin bowling ball is 10.80 cm. Note: bowling balls generally do NOT have a uniform mass distribution, you should not assume that Roberto's ball does have a uniform distribution of mass. Roberto is a novice bowler and releases the ball with very little spin. He notices that, once the ball leaves his hand, it always begins its trip toward the pins by slipping (or sliding) along the surface of the lane; and, as it slides, the spin rate is gradually increasing. At some point along the lane, the spin rate exactly correlates with the speed of the ball and the ball begins to roll without slipping. Roberto notices that, for his throws, rolling without slipping always begins at about the same location along the lane. Stepping off the distance, he finds that the distance from his release point to the "rolling-without-slipping point is about 5.639 m (the distance from the foul line to the head pin is 18.29 m). Eager to estimate his release speed, he asks his friend Sharon to measure the time between release and rolling-without-slipping. Sharon takes measurements of the time interval for several of Roberto's throws, and arrives at an average of 1.015 seconds. At this particular bowling alley, the pins are due West of the bowlers.