1. Advanced Physics Chapter 5 Circular Motion: Gravitation

2. Chapter 5: Circular Motion: Gravitation z5-1 Kinematics of Uniform Circular Motion z5-2 Dynamics of Uniform Circular Motion z5-3 Highway Curves, Banked and Unbanked z5-4 Nonuniform Circular Motion z5-6 Newton’s Law of Universal Gravitation z5-7 Gravity near the Earth's Surface z5-8 Satellites and “Weightlessness” z5-10 Types of Forces in Nature

3. 5-1 Kinematics of Uniform Circular Motion Uniform Circular Motion zobject that moves in a circle with constant speed zmagnitude of velocity is constant but direction is changing

4. 5-1 Kinematics of Uniform Circular Motion Centripetal (radial) acceleration (a r or a c ) zcenter-seeking acceleration zacceleration directed toward the center of the circle zvelocity and acceleration vectors are perpendicular to each other

5. 5-1 Kinematics of Uniform Circular Motion Velocity zv = d/t zd = 2  r zso v = 2  r/T zwhere T = period of revolution (sec) zand f = frequency (sec -1 ) zT = 1/f

6. 5-1 Kinematics of Uniform Circular Motion Centripetal acceleration za R = v 2 /r za R = 4  2 r/T 2

7. 5-2 Dynamics of Uniform Circular Motion According to Newton’s Second Law: F net = ma z  F R = ma R = mv 2 /r znet centripetal force (  F R ) must be directed toward center (why?) zcentripetal force vs. centrifugal force

8. 5-3 Highway Curves, Banked and Unbanked zWhen a car goes around a curve in the road what keeps it on the road? zWhen is the friction between the tires and the road greater, when they are rolling or sliding? zSo to keep a car on the road on a curve we must……

9. 5-3 Highway Curves, Banked and Unbanked zBanking a curve reduces skidding why? zF n is at an angle toward the center of the curve zso a portion of the F n goes into F R so the tires need to supply less frictional force to make up for the remaining F R needed

10. 5-3 Highway Curves, Banked and Unbanked Banking angle of road zF n sin  = mv 2 /r zsince F n cos  = mg then F n = mg/cos  zmg(sin  /cos  ) = mv 2 /r zg(tan  ) = v 2 /r ztan  = v 2 /rg zso banking angle of road doesn’t depend on m, just v,r and g

11. 5-4 Nonuniform Circular Motion zFor an object in UCM; the only acceleration is due to radial (centripetal) acceleration za R is caused by what? Equation? zBut if the object in circular motion is speeding up or slowing down there is another type of acceleration, tangential acceleration

12. 5-4 Nonuniform Circular Motion Tangential acceleration (a tan ) zAcceleration caused by the change in the magnitude of the velocity of an object moving in a circular path za tan =  v/  t

13. 5-4 Nonuniform Circular Motion Total vector acceleration (a) zAcceleration caused by the change in the magnitude and direction of the velocity of an object moving in a circular path zIt is the sum of both the tangential and radial acceleration of an object za = a tan + a R

14. 5-4 Nonuniform Circular Motion Total vector acceleration (a) za = a tan + a R The magnitude of a at any moment is: za = (a 2 tan + a 2 R ) 1/2

15. 5-6 Newton’s Law of Universal Gravitation Newton’s Law of Universal Gravitation zevery particle in the Universe attracts every other particle with a force that is proportional to their masses and inversely proportional to the distance between them

16. 5-6 Newton’s Law of Universal Gravitation Newton’s Law of Universal Gravitation zthe force of gravity acts along a line joining the two particles. zF = Gm 1 m 2 /d 2 zG = 6.67 x10 –11 Nm 2 /kg 2

17. 5-6 Newton’s Law of Universal Gravitation zFind the force of gravity between two electrons that are 2.3x10 -2 nm apart zAnswer: y1.05 x 10 -49 N

18. 5-7 Gravity near the Earth's Surface zSince the force of gravity is equal to the weight of an object… zGm o m e /r 2 = m o g zso…. zg = Gm e /r 2 zso..gravity (g) doesn’t depend on the mass of the object, just G, m e and r!

19. 5-8 Satellites and “Weightlessness” zWhy do satellites orbit the Earth? zHow can a person orbiting the Earth experience “weightlessness”? zMany nasty effects of weightlessness on the body

20. 5-8 Satellites and “Weightlessness” zWhat is the relationship between F n, F a, and F g in the following situations? zstationary zaccelerating up zaccelerating down zin free-fall

21. 5-10 Types of Forces in Nature Four different fundamental forces: zgravitational force yforce between any two objects zelectromagnet force yforce between any two charged objects zstrong nuclear force yforce that holds the nucleus together zweak nuclear force yforce involved in certain types of nuclear decay

22. 5-10 Types of Forces in Nature What is GUT?