Question

The angular velocity of a point on a circle with a diameter of 24 feet is 15π radians per second. Find the approximate speed of the point on the circle. 2.5 ft/sec 3.9 ft/sec 565 ft/sec 1,131 ft/sec

Answer 1

Given

angular velocity of a point on a circle is 15π radians per second

diameter of circle 24 feet

Find the approximate speed of the point on the circle

To proof

Radius of circle = 12 feet

angular velocity of a point on a circle =  15π radians per second

FORMULA

$Angular\ velocity\ (\omega)= \frac{V}{r}$

where V  = Linear velocity

          r = radius of the circle

put values in the above equation

we get

$15\Pi = \frac{V}{12}$

V = 12× 15п  

( π = 3.14)

put this in the above equation

we get

V = 12 × 15 × 3.14

 = 565.2 feet per second

Thus approximate speed of the point on the circle  565 feet per second

Hence proved