The rotational motion. The period and frequency.
Frequency is the number of occurrences of a repeating event per unit time. The period is the
duration of one cycle in a repeating event, so the period is the reciprocal of the frequency.
Loosely speaking, 1 year is the period of the Earth's orbit around the Sun, and the Earth's rotation on
its axis has a frequency of 1 rotation per day.
Definitions and units
For cyclical processes, such as rotation,
oscillations, or waves, frequency is defined as
a number of cycles per unit time. In physics
and engineering disciplines, such as optics,
acoustics, and radio, frequency is usually
denoted by a Latin letter f or by a
Greek letter γ (nu).
In SI units, the unit of frequency is hertz (Hz), named after the German physicist Heinrich Hertz.
1 Hz means that an event repeats once per second. A previous name for this unit was cycles per second.
A traditional unit of measure used with rotating mechanical devices is revolutions per minute,
abbreviated RPM.
60 RPM equals one hertz.
Time passing for one revolution is called period. The unit of period is second. T is the representation of
period.
The period, usually denoted by T, is the length of time taken by one cycle, and is the reciprocal of the
frequency γ :
Т = 1/γ
Angular Speed:
We define angular velocity as “change of the angular displacement in a unit of time”. One total rotation
corresponds to 2π radians. Units of angular speed are revolution per unit time radians per second. We show
angular speed with the Greek letter “ω” omega. All points on the platform have same angular velocity.
Average Speed=2π/T
ω=2π/T=2π γ
EXAMPLE
The earth makes a complete rotation around the sun once every 365.25 days. what is the
earth’s angular velocity?
The
The question tells us that the Earth has a period of T = 365.25 days. If we plug this value into the
equation relating period and angular velocity, we find:
ω =2π/T = 2π/365,25 days = 1,7202* 10-2 1/days
http://en.wikipedia.org/wiki/Frequency
frequency – частота
period – період
repeat – повторення
reciprocal – обернена величина
rotation – обертання
oscillations - коливання
waves – хвилі
revolutions per minute – оберти за хвилину
cycle – оберт (цикл)
1. Hamlet, a hamster, runs on his exercise wheel, which turns around once every 0,5 sec.
What is the frequency of the wheel?
T=0,5 sec,
γ= 2 Hz
2) A sock stuck to the inside of the clothes dryer spins around the drum once every 2.0
sec at a distance of 0,5 m from the center of the drum. What is the socks linear speed?
T= 2 sec, r = 0,5 m, Circum= 2 π r =Dist, so V=2 π r /T = 1.57 m/s
If the drum were twice as wide, but continued to turn with the same frequency, would the
linear speed of a sock stuck to the inside be faster, slower, or the same?
Speed twice as fast (circ twice)
3) What is the radius of an automobile that turns with a frequency of 11 Hz and has a
linear speed of 20 m/s ?
γ = 11 Hz, T = 1/11 sec, V=20 m/s = 2 π r /T or 2 π r * γ = 2* π *r*11= 20, r = 289 mm