The Angular Frequency of a Physical Pendulum calculator computes the approximate value of the angular frequency given that the amplitude of the pendulum is small.
INSTRUCTIONS: Choose your preferred units and enter the following:
- (m) This is the mass of the pendulum
- (d) This is the distance from the pivot point to the center of gravity
- (I) This is the moment of inertia
Angular Frequency(ω): The calculator returns the angular frequency in units of "per/minute".
The Math / Science
The formula used in this calculator is as follows:
`omega = sqrt((m*g*d)/I)`
A physical pendulum is a body or mass suspended from a rotation point as shown in the figure. The gravitational force acts on the body at the center of gravity. This formula employs the acceleration due to gravity at sea-level on Earth (g = 9.80665 m/s²)
Envision how the two component forces change as the pendulum swings. The force of gravity `m*g` remains constant, while the force acting to return the body to equilibrium, `m*g*sin(theta)`, increases to it's maximum value (equal to `m*g`) at `theta` = 90o.
Moment of Inertia
vCalc has many formulas to compute the Moment of Inertia of different shapes. The Moment of Inertia library can be found HERE. A calculator with many of the MOI equations can be found HERE.
Reference
Young, Hugh and Freeman, Roger. University Physics With Modern Physics. Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 438, eq 13.38