Question

40. A pendulum in a museum swings through

an angle of 60° in 17.3 s. The linear velocity
of the pendulum is 1.32 ft/s. Determine the
length of the pendulum.

Answer 1

21.81 ft

Explanation:

For an arc of measure α and radius r, the arc length is ...

s = r·α . . . . . . where α is in radians

Then the linear speed is ...

s' = r·α'

Here the rate of change of arc angle is (π/3)/(17.3) rad/s, so the radius can be found to be ...

r = s'/α/ = (1.32 ft/s)/((π/3)/17.3 rad/s) = 1.32·3·17.3/π ft

r ≈ 21.81 ft

The length of the pendulum is about 21.81 feet.