1. Understand Angular Velocity
Angular velocity (ω) is the rate at which an object rotates or revolves around a central point. It's measured in radians per second (rad/s).
2. Calculate the Angle
* The pendulum swings through an arc of 14.13 feet.
* The circumference of the circle the pendulum makes is 2πr (where r is the length of the pendulum).
* The ratio of the arc length to the circumference gives the angle (in radians) the pendulum swings through:
Angle (θ) = (Arc Length) / (Circumference) = 14.13 feet / (2 * 3.14 * 6 feet) = 0.375 radians
3. Calculate Angular Velocity
* Angular velocity is the angle swept out per unit time:
ω = θ / t = 0.375 radians / 3 seconds = 0.125 radians/second
Therefore, the angular velocity of the 6-foot pendulum is 0.125 radians/second.
