- #1

arierreF

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## Homework Statement

I have a physical pendulum that is rotating about an fixed axis.

The period is:

[itex]T=2\pi \sqrt{\frac{I}{mgd}}[/itex]

I = moment of inertia

d = distance between the center of mass and the axis. The problem is:

If you add a mass in the end of the pendulum. The period is going to increase or decrease. My attempt:

the inertia of a rod (physical pendulum)

[itex]I = md^{2} + \frac{1}{12}mL^{2}[/itex]Without the mass, the moment inertia is :

[itex]d = \frac {L}{2}[/itex] the center of mass in in the middle of the physical pendulum.

[itex]I = m\frac {L^{2}}{4} + \frac{1}{12}mL^{2}[/itex]

[itex]I = \frac{1}{3} mL^{2}[/itex]if i add a mass in the end of the pendulum then

[itex]I = mL^{2} + \frac{1}{12}mL^{2}[/itex]

[itex]I = \frac {13}{12} mL^{2}[/itex]without mass:

[itex]T=2\pi \sqrt{\frac{\frac{1}{3} mL^{2}}{mg\frac{L}{2}}}[/itex]

[itex] T=2\pi \sqrt{\frac{2L}{3g}} [/itex]

with mass:

[itex]T=2\pi \sqrt{\frac{\frac {13}{12} mL^{2}}{mgL}}[/itex]

[itex]T=2\pi \sqrt{\frac {13L}{12g} }[/itex]

If we add a mass in the end of the physical pendulum, then the period is going to increase.Can somebody check if my answer is correct?