Concept explainers
(a)
Find the period of the pendulum for each horizontal axis.
(a)
Answer to Problem 103P
The period of the pendulum for each horizontal axis is
Explanation of Solution
Write the equation for time period of the physical pendulum.
Here,
Write the equation of the moment of inertia for uniform rod.
Here,
Conclusion:
Substitute equation (II) in equation (I) and replace
Substitute
Therefore, the time period of the pendulum for each horizontal axis is
(b)
Find the period of the pendulum for two rods.
(b)
Answer to Problem 103P
The time period of the pendulum for two rods is
Explanation of Solution
Consider the meter stick as two rods with lengths
Write the equation of the moment of inertia for
Here,
Write the equation of the moment of inertia for
Rewrite the equation (III).
Rewrite the equation (IV)
The total inertia of the two rods is.
Conclusion:
Substitute
Substitute
Therefore, the time period of the pendulum for two rods is
(c)
Find the period of the pendulum for two rods.
(c)
Answer to Problem 103P
The time period of the pendulum for two rods is
Explanation of Solution
Consider the meter stick as two rods with lengths
Write the equation of the moment of inertia for
Write the equation of the moment of inertia for
Rewrite the equation (V).
Rewrite the equation (VI)
The total inertia of the two rods is.
Conclusion:
Substitute
Substitute
Therefore, the time period of the pendulum for two rods is
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