Clarification: What meant by expression is that you can choose one of the common

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Clarification: What meant by expression is that you can choose one of the common moment of inertia for the pendulum and use it in that formula...

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It can be shown (for example, see your textbook) that for a general pendulum system, the period can be described as: period-T = 2 MgR Where: I is the moment of inertia of the pendulum (About an axis through its point of support and perpendicular to its plane of swing) m is the mass of the pendulum r is the distance between the pivot point and the center of mass of the pendulum. Note; some common expressions of1 are given in the table on the next page 7. Using this theoretical expression, what is the period of a simple pendulum? Elaborate on which expression you chose to use for I.

Explanation / Answer

Time period of a physical pendulum,

T = 2*pi*sqrt(I/(M*g*R))

here I is the moment of inertia of the abject about the axis of rotation.

M is the mass of the body.

R is the distance from axis of rotation to center of mass of the body.

In the case of simple pendulum the bob acts as a point particle.

so, I = M*L^2 and R = L

so,

T = 2*pi*sqrt(M*L^2/(M*g*L))

T = 2*pi*sqrt(L/g) <<<<<<<<<<<-------------Answer

here L is the length of the pendulum.

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