Physical Pendulum Calculation  



Center of Mass or Moment of Inertia:
I = T^{2} MgD/4 ∏^{2}
Mass:
M = 4 ∏^{2}I/gDT^{2}
Acceleration of Gravity:
g = 4 ∏^{2}I / MDT^{2}
Distance from Center of Mass to Pivot:
D = 4 ∏^{2}I / Mg T^{2}
Where,
T = Period,
I = Center of Mass or Moment of Inertia,
M = Mass,
g = Acceleration of Gravity,
D = Distance from Center of Mass to Pivot.
Example:
Calculate the time Period taken by a Physical Pendulum to rotate by the given details of the pendulum.
Center of Mass or Moment of Inertia (I) = 25 kgm^{2}
Mass (M) = 15 kg
Acceleration of Gravity (g) = 10 m/s^{2}
Distance from Center of Mass to Pivot (D) = 5 m
Solution:
Apply Formula:
T = 2∏√(I/MgD)
T = 2*3.14 √(25/15*10*5)
T = 6.28 √(25/750)
T = 6.28 √0.033
T = 6.28*0.182
T = 1.1429
T = 1.15 s
Period (T) = 1.15 s