Pendulum Length

The length of the pendulum in the clock can be found by knowing the angle between the maximum points of the pendulum and the distance covered by the pendulum. The length of the pendulum can be calculated using the arc length formula where the known values are the central angle and the distance covered by the pendulum between the maximum points. In the following article we will see in detail about the topic pendulum length.

pendulum
More about Pendulum Length:

The pendulum oscuillstes from a single point and the pendulum covers a maximum position on the each side and the angle between the maximum positions can be measured and the distance covered by the pendulum between the maximum positions is also measured. Using all the values and substituting these values in the arc length formula we can calculate the length of the pendulum from the formula.

The formula for the arc length L = (theta/360)*2*pi*r

Here the θ is the angle between the maximum positions and r is the length of the pendulum and L is the distance covered by the pendulum between the maximum positions.
Example Problems on Pendulum Length:

1. The angle covered between the maximum positions of pendulum and the distance covered between the maximum positions are 110 degrees and 20 cm. Find the length of the pendulum.

Solution:

The length of the pendulum = (360*L)/(2*pi*theta)

= (360*20)/(2*pi*110)

= 360/11*pi

= 10.4 cm

2. The angle covered between the maximum positions of pendulum and the distance covered between the maximum positions are 120 degrees and 25 cm. Find the length of the pendulum.

Solution:

The length of the pendulum = (360*L)/(2*pi*theta)

= (360*25)/(2*pi*120)

= (3*25)/(2*pi)

= "12 cm"
Practice problems on pendulum length:

1. The angle covered between the maximum positions of pendulum and the distance covered between the maximum positions are 100 degrees and 18 cm. Find the length of the pendulum.

Answer: 10.3 cm.