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?
A)47.7 rpm
B)955 rpm
C)72.0 rpm
D)50.0 rpm
E)100 rpm

Question

Quizplus · Accepted Answer

The angular speed ($\omega$) in revolutions per minute (rpm) can be found by converting the linear speed (v) to angular speed using the formula $\omega = \frac{v}{r}$, where $r$ is the radius of the wheel. Given the diameter is 120 mm, the radius $r = 60$ mm or $0.06$ m. Since $v = 6.00$ m/s, converting $v$ to meters per minute (by multiplying by 60), we get $360$ m/min. Thus, $\omega = \frac{360 \, \text{m/min}}{0.06 \, \text{m}} = 6000$ revolutions per minute. However, this calculation seems to have an error in unit conversion or interpretation of the formula, as the correct approach should involve the relationship $\omega = \frac{v}{r}$ with proper unit conversion for angular speed to rpm. The correct calculation involves using the circumference of the wheel to determine how many revolutions per second and then converting to rpm. The correct formula considering the circumference ($C = \pi \times \text{diameter}$) for conversion from linear speed to rpm is $\omega = \frac{v}{C} \times 60$, leading to the correct answer being 955 rpm after correctly applying unit conversions and the relationship between linear speed, wheel size, and angular speed.

A Scooter Has Wheels with a Diameter of 120 Mm