Professional skateboarder Leticia Bufoni does a 360 kickflip in $0.24 \mathrm{~s}$, where her board rotates a full $360^{\circ}$ around while also flipping once. Ignoring the flipping motion and just considering the rotation, what is the average angular velocity of her board?
$1500 \mathrm{rad} / \mathrm{s}$
$13 \mathrm{rad} / \mathrm{s}$
$26 \mathrm{rad} / \mathrm{s}$
$86 \mathrm{rad} / \mathrm{s}$
Answer
Final Answer: The average angular velocity of her board is \(\boxed{26.18 \, \mathrm{rad/s}}\).
Step 1 ：The average angular velocity can be calculated by dividing the total angle of rotation by the time taken. In this case, the total angle of rotation is 360 degrees, which is equivalent to \(2\pi\) radians. The time taken is 0.24 seconds.
Step 2 ：Therefore, the average angular velocity is \(\frac{2\pi}{0.24}\) rad/s.
Step 3 ：After calculating, we find that the average angular velocity is approximately 26.18 rad/s.
Step 4 ：Final Answer: The average angular velocity of her board is \(\boxed{26.18 \, \mathrm{rad/s}}\).
