chapter 16 - circular motion

Question 1

360 degrees

Answer 1

2pi

Question 2

units of angular velocity

Answer 2

SI = rad/sec
rev/s

Question 3

angular velocity

Answer 3

rate of change of an angle
⍵ = Δθ/t
= 2𝞹/T
= 2𝞹f

Question 4

requirement for uniform circular motion

Answer 4

force perp to velocity
(centripetal force)

Question 5

linear velocity

Answer 5

v = 2𝞹r/T
= ⍵r

Question 6

how does an object accelerate but still travel at constant speed

Answer 6

acceleration is perp to velocity - direction changes so velocity changes but speed remains the same

Question 7

centripetal force in - a car turning, the moon and a banked track

Answer 7

• friction
• gravitational attraction of Earth
• horizontal component of the normal reaction + friction

Question 8

if a mass is in a verticle circle where is tension greatest and least

Answer 8

greatest = bottom
least = top

Question 9

centripetal force

Answer 9

any force that keeps a body moving with uniform speed in a circular path
always perp to velocity
- so has no component in the direction of motion and does no work
- so speed is constant
F = mv²/r
= m⍵²r

Question 10

centripetal acceleration

Answer 10

acts towards the centre of the circle
acceleration of an object moving with uniform speed in a circular path
a = v²/r
= ⍵²r

Question 11

verify F =mv^2/r

Answer 11

have a bung on a string with washers on the other end and a tube so the bung swings
F = tension due to weight of washers (Mg)
m = mass of bung
r = radius of circle
v = velocity of bung
find v by recoring with stop wqatch in frame and counting revolutionds - make sure circule is horizontal and wrist still
find the time for 30 rotations form the video T = t/30
v = 2pir/T
plot F against v^2
grad = m/r
m = grad*r is measured m = experimental m then verified

Question 12

conical pendulum

Answer 12

Tsinθ = mv^2/r
Tcosθ = mg
Tension provides centripetal force

Question 13

vertical circle

Answer 13

at diff parts the centripetal force is made up of combinations of R and mg
(inside)
eg top F = mg + R
bottom F = R-mg
side F = W
(on this at top R = 0)
outside
opposite for top and bottom

Question 14

banked circle eg velodrome

Answer 14

Rcosθ = mv^2/r
a component of R is the centripetal force
weight is perp so isnt a factor

Question 15

humpback bridge

Answer 15

if the car goes too fast it leaves the circle
W = mv^2/r
as W,m,r are fixed if v increases too much theres not enough centripetal force from W so it leaves the orbit