A platter rotates with a period of 3.86 s , and has a radius of 15.1 cm . What is the velocity of the platter? \[ v=[?] \mathrm{cm} / \mathrm{s} \]

To find the velocity of the platter, we can use the formula for linear velocity in circular motion, which is given by \( v = \frac{2\pi r}{T} \), where \( r \) is the radius, and \( T \) is the period. Plugging in the values: \( r = 15.1 \) cm and \( T = 3.86 \) s, we get: \[ v = \frac{2\pi \times 15.1 \text{ cm}}{3.86 \text{ s}} \approx \frac{94.67 \text{ cm}}{3.86 \text{ s}} \approx 24.5 \text{ cm/s} \] So the velocity of the platter is approximately \( 24.5 \, \text{cm/s} \). One common mistake when calculating velocity in circular motion is forgetting to convert units properly. Make sure that when you're dealing with the radius, if you had it in meters, to convert it to centimeters (or vice-versa) so your calculations remain consistent. Always double-check unit conversions to avoid conflicts in your final answer!