The end of a 30 inch pendulum describes an arc of 6 inches through what angle does the pendulum swing?
arc=angleinradians*radius
solve for angleinradians
To determine the angle through which the pendulum swings, we can use the concept of a sector of a circle.
First, let's define the variables:
- Arc length: l = 6 inches
- Radius of the pendulum: r = 30 inches
- Angle through which the pendulum swings: θ (in radians)
The formula to find the length of an arc in a circle is:
l = rθ
Rearranging the formula to solve for θ:
θ = l / r
Plugging in the given values:
θ = 6 / 30
θ = 0.2 radians
So, the pendulum swings through an angle of 0.2 radians.