# Rotational Acceleration of a Physical Pendulum

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(d^2theta)/(dt^2) =
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Billy.Rotational Acceleration of a Physical Pendulum
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The Rotational Acceleration of a Physical Pendulum calculator approximates the rotational acceleration of a physical pendulum based on the mass (m), acceleration due to gravity (g), distance to the center of gravity (d), impulse (I) and the angle (Θ).

INSTRUCTIONS: Choose the preferred units and enter the following:

• (m)  This is the mass.
• (d)  This is the distance to the center of gravity.
• (Θ) This is the angle of displacement.
• (I) This is the inertia.

Rotational Acceleration: The calculator returns the acceleration in radians per second squared (rad/s2).  However this can be automatically converted to compatible units via the pull-down menu.

#### The Math / Science

The Rotational Acceleration of a Physical Pendulum equation calculates the rotational acceleration of the physical pendulum given that θ is small. This is because sinθ is approximately θ. So this equation will give the approximate rotational acceleration given that the angle is small.

# References

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 13.37