16 - Circular Motion

Question 1

explain how an object moving with circular motion at a constant speed has an acceleration

Answer 1

direction of the velocity is constantly changing, change in velocity means it is accelerating

Question 2

uniform circular motion: v =

Answer 2

v=2πr/T or v=2πrf

Question 3

define angular displacement

Answer 3

angle swept out at centre of circular path

Question 4

angular velocity equation, units

Answer 4

ω=θ/t
measured in rads^-1

Question 5

radian defined as…

Answer 5

angle swept out when s = r (arc radius)
s=θr

Question 6

other units for angular speed

Answer 6

revolutions per second (revs^-1) or revolutions per minute (r.p.m.)

Question 7

angular frequency

Answer 7

is the same as angular speed
ω=2π/T or ω=2πf

Question 8

relationship between angular and linear speed

Answer 8

ω=2π/T > T=2π/ω
v=2πr/T
sub T from 1st > v=rω
linear speed = radius x angular speed

Question 9

in what direction is centripetal force

Answer 9

towards centre

Question 10

in what direction is the acceleration

Answer 10

towards centre, perpendicular to velocity direction

Question 11

acceleration equation derivation

Answer 11

a=v^2/r and v=rw
so a=r2w2/r
a=rw^2

v=rw
so a=vw

Question 12

circular motion occurs due to

Answer 12

force acting perpendicular to direction of motion (towards centre) causing an acceleration is that perpendicular direction also

Question 13

equations for centripetal force

Answer 13

F=ma (subbing a=v^2/r or a=rw^2 or a=vw)
F=mv^2/r
F=mrw^2
F=mvw

Question 14

force effect perpendicular direction of centre

Answer 14

weight is perpendicular to direction of centre so no effect on centripetal force

Question 15

centripetal force is a combo of

Answer 15

vector sum of tension and weight