an object is travelieng on a circle with a radius of 2 meters. If in 20 seconds the object travels 5 meters. What is the angular velocity?

Question

An object is traveling on a circle with a radius of 2 meters.  If in 20 seconds the object travels 5 meters...what is the angular velocity

Answer 1

The arc length is related to the radius and angle (in radians) by the formula, s = rθ.

 

θ = s/r = 5m/2m = 2.5 rads

 

The angular velocity (speed) is then the angle advanced divide by the time it took: ω = θ/t = 2.5 rads/20 s = 0.125 rads/s

Answer 2

(5m/2m)(2π radians)/20 s = 10π rad / 40 s = π/4s

Answer 3

5 meters/2 meters = 2.5 times around the circle.  Since there are 360^o in once around, the object travels through 360^o*2.5 = 900 degrees.  The angular velocity would be:

 

900^o/20 sec = 45^o per sec = pi/4 radians per second