1. Topic 6 Circular motion and gravitation 2013-2014 HONOR PHYSICS

2. Content 6.1 Circular motion 6.2 Newton ’ s law of gravitation Rev iew

3. 6.1 Circular motion

4. 6.1 Circular motion

5. 6.1 Circular motion

6. Angular displacemen t The angle moved around the circle by an object from where its circular motion starts. It ’ s not a vector. Unit : degrees () or radians ( rad ) 1 degree is defined to be 1/360 th of the way around a circle. 1 radian is defined as the angle equal to the circumference of an arc of circle divided by the radius of the circle. 360=2 π =6.28 rad And 1 rad =57.3 6.1 Displacemen t, velocity, period, frequency Centrip etal force Centripeta l accelerati on Turning and banking Moving in a vertica l circle

7. Angular velocity 6.1 Displacemen t, velocity, period, frequency Centrip etal force Centripeta l accelerati on Turning and banking Moving in a vertica l circle Unit : radians per second ( rad s -1 )

8. 6.1 Displacemen t, velocity, period, frequency Centrip etal force Period and frequency Centripeta l accelerati on Turning and banking Moving in a vertica l circle Periodic time / period, T The time taken for the object to go round the circle once. Frequency, f Number of times an object goes round a circle in unit time Unit : Hertz ( Hz = s -1 )

9. 6.1 Displacemen t, velocity, period, frequency Centrip etal force Centripeta l accelerati on Turning and banking Moving in a vertica l circle

10. 6.1 Displacemen t, velocity, period, frequency Centrip etal force Centripeta l accelerati on Turning and banking Moving in a vertica l circle When the circle has a radius r the circumference is 2 πr. T is the time taken to go around once. So he linear speed of the object along the edge of the circle v is And so Linking angular and linear velocity

11. 6.1 Displacemen t, velocity, period, frequency Centrip etal force Centripeta l accelerati on Turning and banking Moving in a vertica l circle Acceleration is Centripetal acceleration Where does Δv point? To the centre of the circle.

12. 6.1 Displacemen t, velocity, period, frequency Centrip etal force Centripeta l accelerati on Turning and banking Moving in a vertica l circle Apply Newton ’ s second law of motion Centripet al force The force is always directed perpendicular to the direction that the object is being displaced What force provides the centripetal force for that situation?

13. 6.1 Displacemen t, velocity, period, frequency Centrip etal force Centripeta l accelerati on Turning and banking Moving in a vertica l circle Satellites in orbit Centripet al force

14. 6.1 Displacemen t, velocity, period, frequency Centrip etal force Centripeta l accelerati on Turning and banking Moving in a vertica l circle Amusement park rides Centripet al force

15. 6.1 Displacemen t, velocity, period, frequency Centrip etal force Centripeta l accelerati on Turning and banking Moving in a vertica l circle Amusement park rides Turning on a horizontal road

16. 6.1 Displacemen t, velocity, period, frequency Centrip etal force Centripeta l accelerati on Turning and banking Moving in a vertica l circle Bankin g

17. 6.1 Displacemen t, velocity, period, frequency Centrip etal force Centripeta l accelerati on Turning and banking Moving in a vertica l circle What are the forces acting when the motion is in a vertical circle?

18. 6.1 Displacemen t, velocity, period, frequency Centrip etal force Centripeta l accelerati on Turning and banking Moving in a vertica l circle Charge in a magnetic field A charged particle moves in a plane perpendicular to a uniform magnetic field is a in a circular path with constant centripetal acceleration

20. Content 6.1 Circular motion 6.2 Newton ’ s law of gravitation

22. 6.2 Gravita tional field strengt h Gravita tional force revisit ed Newton ’ s law of gravit ation Forces that act at a distance Gravity acts at a distance and is an example of a force that has an associated force field. Electri cal field Magneti c field Orbits and gravity

23. 6.2 Gravitational force Imagine two masses in deep space with no other masses close enough to influence them. A is in the gravitational field due to B and a force acts on A. B is in the gravitational field due to A and a force acts on B. These two forces have an equal magnitude but act in opposite directions. Gravita tional field strengt h Gravita tional force revisit ed Newton ’ s law of gravit ation Orbits and gravity

24. 6.2 Gravitational field strength Small test mass : so small that it does not disturb the field being measured. Gravitational field strength at a point is the force per unit mass experienced by a small point mass placed at that point. Unit : N kg -1 Vector quantity, its direction is that of F Gravita tional field strengt h Gravita tional force revisit ed Newton ’ s law of gravit ation Orbits and gravity

25. 6.2 Adding field strengths vectorially What if there is more than one point mass, excluding the test mass itself? Gravita tional field strengt h Gravita tional force revisit ed Newton ’ s law of gravit ation Orbits and gravity

26. 6.2 g and the acceleration due to gravity Gravitational field strength Acceleration due to gravity Gravita tional field strengt h Gravita tional force revisit ed Newton ’ s law of gravit ation Orbits and gravity

27. 6.2 Newton ’ s law of gravitation Newton realized that the gravitational force F between two objects with masses M and m whose centres are separated by distance r is : Always attractive Proportional to 1/ r 2 Proportional to M and m This can be summed up in the equation universal gravitational constant, G =6.67 × 10 -11 N m 2 kg -2 Gravita tional field strengt h Gravita tional force revisit ed Newton ’ s law of gravit ation Orbits and gravity

28. 6.2 Gravita tional field strengt h Gravita tional force revisit ed Newton ’ s law of gravit ation Orbits and gravity

29. 6.2 Gravita tional field strengt h Gravita tional force revisit ed Newton ’ s law of gravit ation Orbits and gravity

30. 6.2 Gravitational field strengths re - visited The field strength at a distance r from a point mass, M Gravita tional field strengt h Gravita tional force revisit ed Newton ’ s law of gravit ation Orbits and gravity

31. 6.2 Gravitational field strengths re - visited The field strength at a distance r from the centre outside a sphere of mass M Gravita tional field strengt h Gravita tional force revisit ed Newton ’ s law of gravit ation Orbits and gravity

32. 6.2 Linking orbits and gravity Newton ’ s cannon – how he thought about orbits Gravita tional field strengt h Gravita tional force revisit ed Newton ’ s law of gravit ation Orbits and gravity

33. 6.2 Linking orbits and gravity What if the cannon ball is fired at even greater speeds? http :// waowen. screaming. net / revision / f orce & motion / ncananim. htm Gravita tional field strengt h Gravita tional force revisit ed Newton ’ s law of gravit ation Orbits and gravity

34. 6.2 Linking orbits and gravity Where M E is the mass of the Earth, r is the distance from the satellite to the centre of the Earth. The speed does not depend on the mass of the satellite. All satellites travelling round the Earth at the same distance above the surface have the same speed. The linear speed of a satellite at a particular radius is Where ω is the angular velocity, and T is the orbital period ( time for one orbit ) of the satellite Gravita tional field strengt h Gravita tional force revisit ed Newton ’ s law of gravit ation Orbits and gravity

35. 6.2 Linking orbits and gravity This result is known as Kepler ’ s third law. Gravita tional field strengt h Gravita tional force revisit ed Newton ’ s law of gravit ation Orbits and gravity

36. 6.2 Gravita tional field strengt h Gravita tional force revisit ed Newton ’ s law of gravit ation Orbits and gravity

37. 6.2 Gravita tional field strengt h Gravita tional force revisit ed Newton ’ s law of gravit ation Orbits and gravity