Circular Motion

Question 1

define angular velocity

Answer 1

ω, the rate of change of angular displacement*

*angle swept in a second

Question 2

angular velocity

Answer 2

ω= θ/t

ω= rad s-1
θ= rad

Question 3

define angular displacement

Answer 3

angle swept through in one second

Question 4

angular displacement

Answer 4

s=rθ

θ= angular displacement
s= arc length

Question 5

angular speed

Answer 5

v = s/t = rθ/t = rω

Question 6

linear velocity

Answer 6

v = ωr

Question 7

why would an object moving with constant speed be accelerating

Answer 7

the direction the object is moving in is continuously changing, therefore velocity is changing -> acceleration

Question 8

periodic time, T

Answer 8

T= s/v = 2π/ω

Question 9

frequency, f

Answer 9

f= 1/T = ω/2π

Question 10

define periodic time

Answer 10

the time taken for particle to travel once around the circle

Question 11

define frequency

Answer 11

number of revolutions made per second

Question 12

what direction is acceleration

Answer 12

always towards the centre of the circle

Question 13

centripedal acceleration

Answer 13

a = vω = v²/r = rω²

Question 14

what is the direction of force

Answer 14

always towards the centre

Question 15

centripedal force

Answer 15

F = ma = mvω = mv²/r = mrω²

Question 16

importance of centripedal force

Answer 16

without it, object would move in a straight line along tangent (centripedal force disappears when object moves in a line)

Question 17

motion in a vertical circle

how to calculate tension at the top of the circle

Answer 17

T and mg are the same direction so:
T + mg = mv²/r
∴
T = mv²/r - mg

Question 18

motion in a vertical circle

how to calculate tension at bottom of the circle

Answer 18

T and mg going opposite direction so:
T - mg = mv²/r
∴
T = mv²/r + mg

Question 19

motion in a vertical circle

where is tension the greatest

Answer 19

when object is at the bottom

Question 20

motion in a vertical circle

how to calculate tension at right and left sides

Answer 20

mg is downwards ∴ does n ot effect tension:
T = mv²/r

Question 21

motion is a vertical circle

how to calculate tension at NE and NW angles

Answer 21

T = mω²r - mg cos/sin*θ

*depending on where θ is

Question 22

notion in a vertical circle

how to calculate tension at SE and SW

Answer 22

T = mω²r + mg cos/sin*θ

*depending on where θ is

Question 23

motion at an angle

how to calculate tension

Answer 23

1. resolve forces as at angle:
   * horz: T cos/sinθ = mv²/r
   * vert: T cos/sinθ = mg
2. use pythagorus to find T at angle

*depending on where θ is

Question 24

motion at an angle

how to show it is not possible for string to be horizontal

Answer 24

T sinθ/ T cosθ = tanθ = mg/mv²÷r or gr/v²

Question 25

motion at an angle

why can the string never be horizontal

Answer 25

θ must be 0 ∴ tanθ = 0 –> for this v² must be infinite (not possible)

Question 26

how to convert radians-degrees

Answer 26

° => rad
times by π/180
rad => °
times by 180/π