A racing motorcycle accelerates at a constant rate from zero to 280 km/h in 39 seconds.If the outer diameter of the motorcycle's wheels is 64 cm and they turn without slipping,the angular acceleration of each wheel is A)5.73 rad/s². B)11.5 rad/s². C)3.12 rad/s². D)22.4 rad/s². E)6.23 rad/s².

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Quizplus · Accepted Answer

The linear acceleration can be calculated using the formula $ a = \frac{\Delta v}{\Delta t} $. Converting 280 km/h to m/s gives approximately 77.78 m/s. Thus, $ a = \frac{77.78}{39} \approx 1.994 m/s^2 $. The angular acceleration $ \alpha $ is given by $ \alpha = \frac{a}{r} $, where $ r $ is the radius of the wheel. The radius is 0.32 m (since diameter is 0.64 m), so $ \alpha = \frac{1.994}{0.32} \approx 6.23 \, \text{rad/s}^2 $.

A Racing Motorcycle Accelerates at a Constant Rate from Zero