Pendulum Properties and Energy Carl Wozniak Northern Michigan University

Pendulum basics A pendulum consists of a weight suspended on a rod, string or wire. When the weight or bob is moved and let go, the pendulum will swing back and forth in a regular periodic motion.

Pendulum motion The period of the pendulum is dependent on the length (L) of the string or wire. The shorter the wire, the greater the frequency or how fast it goes back and forth. The frequency is independent of the amplitude (A) of the swing, provided the initial angle (a) is not large. At larger angles, there is a slight change in the frequency. The frequency is independent of the mass of the bob. In other words a pendulum with a heavy bob will move at the same rate as one with a lighter weight bob. But this only makes sense, since the acceleration of gravity on a falling object is independent of the mass of the object.

Why does the pendulum eventually stop? When a pendulum moves, there is some air resistance on the bob and rod or wire. There is also friction at the pivot point. These resistive forces reduce the amplitude of the swing, such that after a while the pendulum will come to a stop. These forces are called damping forces.

Kinetic and potential energy Kinetic energy is the energy of motion. An object which has motion - whether it be vertical or horizontal motion - has kinetic energy Potential energy is the stored energy of position possessed by an object. Gravitational potential energy is the energy stored in an object as the result of its vertical position (i.e., height). This energy is measured in joules (J).

Joules The Joule is named in honor of James Joule who examined the relationship between heat and energy in the 19th Century. The Joule is the SI unit for measuring energy. A joule is related to the fundamental units in that a joule is 1 kg m 2 /s 2.

Pendulum energy states

Calculating potential energy PE grav = mass X g X height P.E. = Potential energy due to gravity Mass = kg g = 9.8 m/s h = m Determine the potential energy of the shorter pendulum

Calculating kinetic energy K.E. = 1/2 mv 2 K.E = kinetic energy (J) m = mass (kg) v = velocity (m/s)

Foucault pendulum Pronounce FOO ko In 1851 Leon Foucault ( ) devised an experiment with a pendulum that demonstrated the rotation of the Earth. given a perfect setting (e.g. no friction), a suspension pendulum will oscillate in a constant path. However, as the earth rotates, that path appears to change. In reality, what is changing is the world about the pendulum.

Foucault pendulum The time it takes to complete the cycle is dependent on the latitude It takes one full day at either pole, more time as you near the equator