Question

What is the angular velocity of a 6–foot pendulum that takes 3 seconds to complete an arc of 14.13 feet? Use 3.14 for π

Answer 1

1) Calculate the whole arc (complete circumference):


Circumference = 2π*radius


radius = 6 foot


=> Circumference = 2 * 3.14 * 6 foot = 37.68


2) Calculate the time to make a whole round, by making a proportion with the two ratios:


 ratio 1 = x / 37.68 =


ratio 2 = 3 / 14.13


ratio 1 = ratio 2 =>

   x                  3s
----------  =   -----------
37.68 ft        14.13 ft


=> x = 3 * 37.68 / 14.13 = 8 s


3) Calcuate the angular velocity as the 2π rad (which is the total angle of a circle) divided by the time.


So the angular velocity is 2π rad / 8 s = 2*3.14 foot / 8 s = 0.785 rad / s



Answer: 0.785 rad / s