Question

problem 1
a spinning car wheel does 10 revolutions in 0.5 seconds. find the frequency and angular velocity of the spinning wheel.

Explanation:

Step1: Calculate the frequency

Frequency \( f=\frac{n}{t} \), where \( n = 10 \) revolutions and \( t=0.5\ s \).
\( f=\frac{10}{0.5}=20\ Hz \)

Step2: Calculate the angular velocity

Angular velocity \( \omega = 2\pi f \).
Substitute \( f = 20\ Hz \) into the formula: \( \omega=2\pi\times20 = 40\pi\ rad/s\approx 125.66\ rad/s \)

Answer:

The frequency is \( 20\ Hz \) and the angular velocity is approximately \( 125.66\ rad/s \)