Question

a scooter has wheels with a diameter of 120 mm. what is the angular speed of the wheels when the scooter is moving forward at 6.00 m/s?

Answer 1

The speed of the angular wheel is,

\(\begin{aligned} v &=r \omega \\ \omega &=\frac{v}{r} \\ v &=6.00 \mathrm{~m} / \mathrm{s}, r=\frac{d}{2}=\frac{120 \times 10^{-3} \mathrm{~m}}{2}=0.06 \mathrm{~m} \\ \omega &=\frac{6.00 \mathrm{~m} / \mathrm{s}}{0.06 \mathrm{~m}} \\ &=100 \mathrm{rad} / \mathrm{s} \end{aligned}\)

Convert the units from \(\mathrm{rad} / \mathrm{s}\) to rpm.

\(\omega=100\left(\frac{\mathrm{rad}}{\mathrm{s}}\right)\left(\frac{1 \mathrm{rev}}{2 \pi \mathrm{rad}}\right)\left(\frac{60 \mathrm{~s}}{1 \mathrm{mn}}\right)\)

\(=\frac{(100)(60)}{2 \pi} \mathrm{rpm} \quad(\mathrm{rpm}=\) revolution per min \()\)

\(=955.41 \mathrm{rpm}\)