Materials needed:
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A pulley
A string or rope
A weight or small object to attach to the string
A ruler or measuring tape
A stopwatch or timer
Steps:
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Tie one end of the string to the weight and the other end to the pulley.
Set up the pulley so that it is free to rotate.
Hold the weight so that it is stationary and parallel to the ground.
Start the stopwatch or timer.
Release the weight so that it begins to fall, and simultaneously start timing how long it takes for the
weight to reach the ground.
Measure the distance between the pulley and the ground using a ruler or measuring tape.
Calculate the angular momentum of the weight using the formula L = Iω, where L is angular
momentum, I is moment of inertia, and ω is angular velocity.
Calculate the moment of inertia of the system using the formula I = mr^2, where m is the mass of
the weight and r is the distance between the pulley and the center of mass of the weight.
Calculate the angular velocity of the weight using the formula ω = Δθ / Δt, where Δθ is the change in
angle of the pulley during the fall of the weight and Δt is the time it takes for the weight to fall.
Calculate the angular momentum of the weight by substituting the values of I and ω into the
formula L = Iω.
Repeat the experiment several times with different masses or distances between the weight and the
pulley, and record the angular momentum each time.
By varying the mass or distance of the weight from the pulley, you can observe the effect of
changing the moment of inertia on the angular momentum. This experiment demonstrates the
principle of conservation of angular momentum, which states that the total angular momentum of a
system remains constant if no external torque acts on the system.
To measure the angular displacement during the fall of weight manually in the angular monument
experiment using a pulley to calculate angular velocity, you would need to follow these steps:
Set up the experiment: Set up the angular monument experiment by fixing the pulley at a certain height
and attaching a weight to a string that is wrapped around the pulley.
Measure the initial position: Before releasing the weight, use a protractor or some other measuring tool
to measure the initial position of the weight. This will give you a reference point to measure the angular
displacement.
Release the weight: Release the weight and let it fall freely. As it falls, it will cause the pulley to rotate
and this rotation can be used to calculate the angular velocity.
Measure the final position: Once the weight has reached the ground, measure the final position of the
weight using the same measuring tool you used to measure the initial position.
Calculate the angular displacement: To calculate the angular displacement, subtract the initial position
from the final position. This will give you the total angular displacement that the pulley has rotated
during the fall of the weight.
Calculate the angular velocity: To calculate the angular velocity, divide the angular displacement by the
time it took for the weight to fall. This will give you the average angular velocity of the pulley during the
fall of the weight.
Note that these measurements are typically done using sensors and data acquisition systems that can
provide more accurate and precise measurements than manual measurements.