Question

A wheel moves with an angular velocity of 16 radians per second. find the speed of the wheel if its diameter is 28 inches.

Answer 1

Let us gather first all the information:

Let rad = radians, rev = revolution, 2πr = circumference, r = radius

Radius = 2 8/2 = 14 in

Equation:

Speed of the wheel = 16 rad/sec * rev / 2πr

rad*2πr / rev

We will cancel rad, rev, and 2πr

So here’s left:

Speed of wheel = 16r in/sec

= 16 * 14 in/sec

= 224 in/sec

Answer 2

568.96 cm/sec

Explanation:

Given , a wheel moves with angualr velocity (ω) is 16 radian per second .

Diameter of wheel is 28 inches.

Radius of wheel =28/2 inches ( by using this formula Diameter= Radius/2)

Radius of wheel = 14 inches

angular velocity (ω)= 16 radian/ sec

now using formula given below

angular velocity= v/r

where v= speed of wheel

r= radius of wheel

radius given in inches change into centimeter by using 1 inch=2.54 cm

therefore , radius =14inches = 14*2.54 cm

now, put tha value in the formula speed = angular velocity* radius

therefore, the speed of wheel = 16*2.54*14

speed of wheel=568.96cm/sec.