Final answer:
The rotational speed of a bowling ball with a radius of 0.11 m and a translational speed of 7.0 m/s is approximately 63.64 radians per second, calculated by the formula ω = v / r, where ω is the angular velocity and v is the linear velocity.
Step-by-step explanation:
The question asks for the rotational speed of a bowling ball that is rolling without slipping on a flat, horizontal surface. This is a typical Physics problem in the area of rotational motion and kinematics. Given that the mass of the bowling ball is 5.0 kg and its radius is 0.11 m, with a translational speed of 7.0 m/s, we can find the rotational speed using the relationship between translational speed (v) and rotational speed (ω) when an object is rolling without slipping, which is v = ω * r. Here, v is the linear velocity, ω is the angular velocity in radians per second, and r is the radius of the ball.
Since there is no slipping, the point on the ball that is in contact with the ground is momentarily at rest relative to the ground, meaning all the speed of the center of mass is due to the rotating motion around some axis. The rotational speed of the ball (ω) can be found by rearranging the formula to ω = v / r.
Plugging in the values:
Rotational speed ω = 7.0 m/s / 0.11 m = 63.64 rad/s
Therefore, the rotational speed of the bowling ball is approximately 63.64 radians per second.