EF 152 – Physics for Engineers
Spring, 2015
Recitation 2.2 Pendulums
Task 1. Simple Pendulums
A. Set the billiard ball and the steel nut pendulum to the same length. Are the periods the same or different? Is
the period a function of the mass?
B. Measure the period of the billiard ball
pendulum. Now double the length of the string.
How has the period changed?
String Length
Period
g
C. Based on measured periods in Task 1.B,
calculate the value of g.
D. Measure the period of the large pendulum in the atrium. From the measured period, calculate the length of the
pendulum. Is your result reasonable? Length of pendulum _______________
Task 2. Period of an Oscillating Bar
A. Attach the rectangular bar to the rotary motion sensor. Measure the period of oscillation for the bar attached 2
cm, 6 cm, 10 cm, and 14 cm above the center of mass of the rod (each hole is 2 cm apart). Plot period of
oscillation vs. distance of the pivot point from the center of mass, r.
B. Derive a formula for the period of oscillation as a function of r. Also note that from our plot in part A there
appears to be a point where the period is minimized. Using calculus, determine the distance r which would result
in the minimum period of oscillation 0 . Check this value experimentally. Some useful formulas are:
 Mass moment of inertia at the center of a long thin rod (length much greater than thickness)
 Parallel axis theorem: I  I CM  Mr
2
 Period of a physical pendulum: T  2
 Quotient rule for derivatives:
I
Mgr
d  f ( x)  g ( x) f ( x)  f ( x) g ( x)


dx  g ( x) 
g ( x)2
Task 3. And one concept question for Professor Biegalski.
A grandfather clock has a weight at the bottom of the pendulum that can be moved up or
down. If the clock is running slow, what should you do to adjust the time properly?
a. move the weight up
b. move the weight down
c. moving the weight will not matter
d. call Facilities Services for repair
Page 1 of 2
EF 152 – Physics for Engineers
Spring, 2015
Task 4. Baseball Bat Pendulum.
We want to determine the mass moment of inertia of a baseball bat. Obtain the following data.
A. Mass of baseball bat: __________________
B. Hang the baseball bat from a point six inches from the knob, and set it in motion as a physical pendulum.
Period of pendulum: ____________________
C. Place each end of the baseball bat on a scale, using angle iron as supports. (Tare the scales with angle iron).
Use the readings on the scales and statics to determine the location of the center of mass.
Distance from pendulum pivot point to balance point: ______________
Calculate the mass moment of inertia of the baseball bat about the pivot point: _____________________
Calculate the mass moment of inertia of the baseball bat about its center of mass: _____________________
The mass moment of inertia about a point six inches from the knob is the
industry standard. The pendulum method is used to determine the
moment of inertia of a baseball bat by ASTM Standard F2398-11 Test
Method for Measuring Moment of Inertia and Center of Percussion of a
Baseball of Softball Bat.
Calculate the mass moment of inertia of the baseball bat about a point 2.5
inches beyond the knob. _______________________
This is approximately where the pivot point of the bat is during impact with
the ball. (Graph from http://www.acs.psu.edu/drussell/bats/bat-moi.html)
The reason we care about the mass moment of inertia of a baseball bat is that it affects swing speed much more
than bat weight. The following graphs show this (graphs from http://www.acs.psu.edu/drussell/bats/bat-moi.html).
The graph on the left is for bats with essentially the same mass moment of inertia, but different weights. The
graph on the right is for bats with essentially the same weight, but difference mass moments of inertia.
Another property of a bat is the center of percussion. The center of percussion is the point where all the mass
would be concentrated so that a simple pendulum with a mass at this point would have the same period as the
bat. More information is at http://www.acs.psu.edu/drussell/bats/cop.html.
Calculate the center of percussion of the bat, measured from the pivot point 6 inches from the knob.
_______________________
Page 2 of 2