1 Škola: Gymnázium, Brno, Slovanské náměstí 7 Šablona: III/2 – Inovace a zkvalitnění výuky prostřednictvím ICT Název projektu: Inovace výuky na GSN prostřednictvím ICT Číslo projektu: CZ.1.07/1.5.00/ Autor: RNDr. Bc. Miroslav Hruška Tematická oblast: Kinematics of a particle (kinematika hmotného bodu) Název DUMu: Uniform circular motion – A Kód: VY_32_INOVACE_FY.2.17 Datum: Cílová skupina: Žáci středních škol s CLIL výukou fyziky v angličtině Klíčová slova:Circle, centre, radius, circular motion, speed, velocity, period, frequency, angle, radian, angular speed Anotace: Prezentace slouží k vysvětlení problematiky rovnoměrného pohybu po kružnici. Prezentaci je vhodné použít při probírání nového učiva.

Kinematics of a particle 17. Uniform circular motion – A

3 Uniform circular motion  UCM is the simplest case of curvilinear motion  Trajectory is a circle  Velocity is varying!  Speed is constant  Direction of velocity is varying  We know that direction of velocity is given by the tangent drawn to the circle

4 Uniform circular motion  UCM is a periodic motion  The time of one revolution around the circle is referred to as the period (perioda, doba oběhu) and denoted by the symbol T  We refer to the number of revolutions (turns) per a time unit as the frequency f  1 turn per second is called hertz, Hz = s -1

5 Parametres of the circular path  r – radius in m  s – distance in m  ϕ – angle in ° or in rad B r s ϕ O r A

6  Compare speed and velocity at uniform circular motion  Explain what “periodic motion” means  What do we call frequency?  When has a particle got a frequency of 1 Hz?  If a particle travelled an angle of 1 radian on a circle of radius of 2 metres, what distance would it cover? Revision

7  Speed is constant, velocity is varying  Motion that repeats in equal intervals of time  Number of turns per a time unit  When it completes one revolution per second  2 metres Revision - answers

8 Angular speed of a particle  Angular speed equals angle divided by time  In SI, radian per second, rad/s, or s -1, is a derived unit of angular speed  We sometimes use the non-SI unit degree per hour, °/h  7 min > less B ϕ O A

9 Angular speed vs speed  Angular speed can be calculated by  If we compare the formulas and, we can find out that

10 Exercise I  Imagine you are standing at the equator. Find your speed relative to the Earth’s axis.  r = 6378 km  T = 24 h (or better 23 h 56 min)  v = ?  v = 2πr ÷ T = 2π × 6378 ÷ km/h  The speed is about 1670 km/h!

11 Exercise II  Imagine you are standing somewhere in Europe. Can you find your speed and angular speed relative to the Earth’s axis?  T = 24 h (or better 23 h 56 min?)  ω = ?  ω = 360° ÷ T = 360° ÷ 24 h = 15°/h  The angular speed is about 15°/h  v = ? We need r, but we don’t know it!

12 Which formula is correct?

That is all for now Thank you for your attention

14  Materiál je určen pro bezplatné používání pro potřeby výuky a vzdělávání na všech typech škol a školských zařízeních. Jakékoliv další využití podléhá autorskému zákonu. Zdroje:  Bednařík, M., Široká, M. Fyzika pro gymnázia, Mechanika. Dotisk 3. vyd. Praha: Prometheus, s. ISBN  Hornby, A. S. Oxford Advanced Learner’s Dictionary of Current English. 5. vyd. Oxford: Oxford University Press, s. ISBN Autor nezaručuje funkčnost webových odkazů!