Galileo’s Pendulum & Clock
Jon Everett
School of Physics
UNSW
Vincenzo
Galilei
(1520-2 July 1591)
Father of Galileo
Musician/Composer
Experimentalist
Galileo Galilei
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15 February 1564 – 8 January 1642) 78
Physicist, Mathematician, Astronomer
Philosopher, Musician
Experimental Scientist
Pendulum &Pendulum Clock
Galileo discovered the
crucial property that
makes pendulums useful
as timekeepers
Clocks before the Pendulum
• Various methods used for converting kinetic
energy to move indicators to show time
passed.
• All suffered from temperature, pressure and
mechanical limitations.
• There was a need for an independant
regulator.
De Dondi Padova ~1290
Praha Astro Clock 1410
De Dondi’s Astrium 1364
Palazzo Vecchio 1299
Galileo the Clock Mechanic
Galileo helped repair windows and
personally took charge of keeping
the convent clock in good repair.
History of Escapements
•Foliot (~1200)
•Verge (~1275)
•Pin Wheel Detent (Galileo ~ 1641)
•Anchor (Hooke ~ 1657)
•Deadbeat (Graham~1721)
•Grasshopper (Harrison~1722)
•Shortt (twin pendulum ~1922)
Galileo’s Escapement 1641
Huygens
Model of Huygens pendulum
clock, 1656. Huygens devised this
model by attaching a pendulum to
the gears of a mechanical clock.
The regular swing of the pendulum
allowed the clock to achieve greater
accuracy. The hands are turned by
the falling weight, which releases
the same amount of energy with
each tick. Galileo Galilei had
already experimented with
pendulums, but Huygens was the
first to master and profit from it. In
1657, he was granted a patent and a
few were made by Salomon Coster
of The Hague.
This was a great improvement over existing mechanical
clocks; their best accuracy was increased from around 15
minutes a day to around 15 seconds a day.[31] Pendulums
spread over Europe as existing clocks were
retrofitted with them.
Huygens ca 1670
with
second hand dial
Huygens
Pendulum Clock 1652
Physics of the Pendulum
The Simple Pendulum
If a pendulum of mass m attached to a string of length L
is displaced by an angle Ɵ from the vertical.
it experiences a net restoring force
due to gravity:
Fr = - mgsin Ɵ
For small angles, sin Ɵ ≈Ɵ , providing is expressed in radians
(try it on your calculator for = 0.1,0.5,1.0 radians).
In terms of radians
Ɵ = S/L radians
where s is the arc length and L is the length of the string. Thus, for
small displacements, s , the restoring force can be written:
Frestoring = matangential
mg sinθ = matangential
For small oscillations the period of a simple pendulum is
therefore given by
This 19th century model is based
on a drawing by Galileo’s friend
and biographer, Viviani, of an
incomplete pendulum clock which
Galilei Galileo (1564-1642)
designed just before his death. It
represents the first certain known
attempt to apply a pendulum to
control the rate of a clock. The
application of the pendulum to
clock timekeeping during the 17th
century scientific revolution was
one of the most fundamental
advances in the history of time
measurement.
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