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

The angular velocity of a 6-foot pendulum that completes an arc of 14.13 feet in 3 seconds is 0.785 radians/second.

Step-by-step explanation:

To calculate the angular velocity of a 6-foot pendulum that completes an arc of 14.13 feet in 3 seconds, we first need to determine the angle that the pendulum sweeps through during its motion. The formula for calculating the angular displacement θ (in radians) is θ = s/r, where s is the arc length and r is the radius (length of the pendulum). Here, the arc length s is 14.13 feet and the radius r is 6 feet.

θ = 14.13 feet / 6 feet = 2.355 radians.

Next, we use the equation that defines angular velocity, ω, which is ω = θ / t, where t is the time. In this case, t is 3 seconds.

ω = 2.355 radians / 3 seconds = 0.785 radians/second.

The angular velocity of the pendulum is 0.785 radians/second.

Answer 2

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