A ball is attached to a string moving in uniform circular motion. The radius of the motion is 12.7 cm , and the speed of the ball is equal to \( 3.45 \mathrm{~m} / \mathrm{s} \). What is the period of motion for the ball? \[ T=[?] \mathrm{s} \]

To find the period of motion \( T \) of the ball moving in uniform circular motion, you can use the formula for period based on the speed and the radius of the circular path: \[ T = \frac{2\pi r}{v} \] In this case, the radius \( r \) is 12.7 cm, which you need to convert to meters (0.127 m), and the speed \( v \) is 3.45 m/s. Plugging in the values, we get: \[ T = \frac{2 \pi (0.127)}{3.45} \approx \frac{0.798}{3.45} \approx 0.231 \, \text{s} \] So, the period of motion \( T \) for the ball is approximately \( 0.231 \, \mathrm{s} \). Enjoy thinking about how that ball is zipping around in circles!