# circular motion

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1. if a particle , moving along a circle passes an equal arc length in equal time , this is called
uniform circular motion
2. linear velocity
• arc length per unit time
• instantaneous velocity of a body in circular motion
3. v =
• s/t
• where v = linear velocity
• s = arc length
• t = time taken
4. linear velocity is a ... quantity
vector
5. the direction of one point in circular motion is
the tangent direction of the circumference at that point
6. angular velocity/speed
in rotation the angle turned through per second , units radians per second , rad s-1
7. ∅ =
• ∅=s/r
8. one radian is defined as
the angle subtended at the center of a circle by an arc equal length to the radius
9. if we let the arc length become the entire circumference then s =
2pir
10. the angle in radians generated in going around a complete circle is
2pi
11. the angular change in full rotation is
either 360 degrees or 2pi radians
360 degrees
360/2pi
14. 1 degree =
15. angular velocity symbol =
w
16. w =
• v/r
• θ/t
17. time period =
the time a body in circular motion takes to complete one revolution , symbol T , units seconds s
18. frequency
• the number of revolutions per second , symbol f , units hertz , Hz ,
• the reciprocal of time period
• T = 1/f
19. rotational speed =
angular speed/velocity
20. if a body is in uniform circular motion along a circumference of radius r the arc it covers in a period T is
2pir
21. hence the linear velocity , v , =
2pir/T
22. hence w =
2pi/T
23. T =
1/f
24. hence w =
2pif
25. the centripetal force is the
resultant force required to keep an object of mass , m , moving at speed , v , on a circular path of radius r
26. the magnitude of the centripetal force =
mv2/r
27. the magnitude of the centripetal force is .... throughout motion
constant
28. the centripetal force always points
towards the center of the circle and continually changes direction as the object moves
29. from v = wr
F =
• m(wr)2/r
• F = mrw2
30. from w = 2pi/T
F =
• mr(2pi/T)2
• F = 4pi2mr/T2
31. by newtons second law F = ma
• mv2/r = ma
• v2/r = a

• mrw2 = ma
• rw2 = a

• 4pi2mr/T2 = ma
• 4pi2r/T= a
32. the centripetal acceleration vector always points
towards the center and continually changes direction as the object moves
33. s , displacement =
a vector describing the difference in position of two points
34. sometimes the displacement may be
2r (see diagram in notes to know when this applies)
35. a mass on the end of a string is whirled round in a horizontal circle at increasing speed until the string breaks . the subsequent path taken by the mass is a
parabola in a vertical plane
36. for a particle moving with uniform speed the kinetic energy of the particle is
constant
37. w =
2pi x rpm/60
38. if a wheel exceeds maximum rate of rotation the direction of motion of the particle immediately after it leaves the wheel will be at a
tangent
39. mass is always in
kg
40. Figure 4 shows an aircraft which is flying in a horizontal circular path at constant speed (see notes , remember diagram ?) the aircraft has constant speed but not constant velocity explain why
• velocity is a vector quantity  - direction of motion is continually changing
• speed is a scalar quantity - magnitude of motion is constant
41. the aircraft is banked
the horizontal component of the support force is acting as the centripetal force
42. what produces the force necessary to accelerate pilot
reaction with seat/friction between passenger and seat
43. forces when a mass is whirled in a circle in a vertical plane
tension at different points
• (see notes remember diagram ? )
• tension at the top is lowest
• tension at the bottom is highest
• top F = tension + mg
• bottom F = tension - mg
44. 1 Figure 1 shows a space station that simulates gravity (artificial gravity). The station is designed in the shape of a cylinder which rotates about its long axis. (remember diagram)
artificial gravity appears to act .....
centripetal force acts ........
astronaut experiences .......
• outwards from the center towards the wall
• inwards on astronaut
• a reaction force of feet
45. angular displacement =
• angle turned through in a given time
• 2pit/T
• 2pift
46. angular speed/velocity =
angular displacement per second
47. centripetal force for a car going round a roundabout
friction
48. centripetal force for ball on a string
tension in string
49. centripetal force for earth moving round sun
gravity
50. see diagram in notes hard to explain
:)
51. banking reduces centripetal force because
the horizontal component is reduced
52. 15m from axis of rotation means