Question

1. a fan blade tip moves in a 0.18 m radius circle at 50 m/s. find its period.

Explanation:

Step1: Recall circular motion formulas

We know that for circular motion, the speed \( v \) is related to the circumference \( C \) and period \( T \) by \( v=\frac{C}{T} \), and the circumference of a circle is \( C = 2\pi r \), so we can substitute \( C \) into the speed formula to get \( v=\frac{2\pi r}{T} \), and then solve for \( T \): \( T=\frac{2\pi r}{v} \).

Step2: Identify given values

The radius \( r = 0.18\space m \) and the speed \( v = 50\space m/s \).

Step3: Substitute values into the formula

Substitute \( r = 0.18\space m \) and \( v = 50\space m/s \) into \( T=\frac{2\pi r}{v} \):
\( T=\frac{2\times\pi\times0.18}{50} \)

Step4: Calculate the value

First, calculate the numerator: \( 2\times\pi\times0.18\approx 2\times3.1416\times0.18\approx1.131 \)
Then divide by 50: \( T=\frac{1.131}{50}\approx0.0226\space s \) (or more precisely, keeping \( \pi \) as is, \( T=\frac{2\pi\times0.18}{50}=\frac{0.36\pi}{50}= 0.0072\pi\approx0.0226\space s \))

Answer:

The period of the fan blade tip is approximately \( \boldsymbol{0.0226\space s} \) (or \( 0.0072\pi\space s \approx 0.0226\space s \))