Question

60. A wheel of radius 8 inches is rotating 15°/s. What is

Answer 1

Answer:

Linear speed : 2.09 in/s

Angular speed in RPM: 2.5 RPM

Angular speed in rad/s: $\frac{\pi}{12} rad/s$

Step-by-step explanation:

Given:

Radius, r = 8 inches

Angular speed = 15°/s

Let's convert the angular speed to radian/sec using the formula :

$15 \frac{degrees}{sec} * \frac{2 \pi rad}{360 degrees} = \frac{\pi}{12} rad/s$

To find the angular speed in RPM.

In rad/second we have:

$\frac{\pi}{12} rad/s$

Convert to minute, we have:

$\frac{\pi}{12} rad/s * \frac{60 sec}{1 minute} = 5\pi rad/minute$

Number of revolutions per minute =

$5\pi rad/min * \frac{1}{2\pi} = 2.5 RPM$

To find the linear speed:

Let's use the formula.

V = rw

Where,

r = 8 inches

w = $\frac{\pi}{12} rad/s$

$V = 8 * \frac{\pi}{12}$

= 2.09 in/sec.