- #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?