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Triss [41]
3 years ago
6

A large stick is pivoted about one end and allowed to swing back and forth with no friction as a physical pendulum. The mass of

the stick is 4.8 kg and its center of gravity (found by finding its balance point) is 1.4 m from the pivot. If the period of the swinging stick is 9 seconds, what is the moment of inertia of the stick about an axis through the pivot
Physics
1 answer:
Tamiku [17]3 years ago
5 0

Answer:

I = 94.33 kg m^2

Explanation:

Let say the rod is slightly pulled away from its equilibrium position

So here net torque on the rod due to its weight is given as

\tau = mg dsin\theta

since rod is pivoted at distance of 1.4 m from centre of gravity

so its moment of inertia about pivot point is given as

Inertia = I

now we have

I \alpha = mg d sin\theta

now for small angular displacement we will have

\alpha = \frac{mgd}{I}\theta

so angular frequency of SHM is given as

\omega = \sqrt{\frac{mgd}{I}}

now we will have

\frac{2\pi}{9} = \sqrt{\frac{4.8(9.8)1.4}{I}

I = 94.33 kg m^2

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