4 - circular motion 1

Question 1

angular speed

Answer 1

is the rate of change of angle with respect to time
dθ/ dt = w
measured in rad/ sec

Question 2

linear speed related to angular speed

Answer 2

v = rw

Question 3

acceleration

Answer 3

a = vw
a = rw^2
a = v^2 / r

Question 4

resultant force

Answer 4

mw^2r
mv^2/r
centripetal force (acts towards the centre)

Question 5

banked tracks

Answer 5

forces acting are R(contact force) and my
resolve R vertically and horizontally then solve

Question 6

displacement in terms of angle and r

Answer 6

s = rθ

Question 7

friction

Answer 7

opposes motion
max friction depends on reaction force
Fmax = μR (point of slipping)
F <= μR
as object moves F increases until max
when force > max friction the object moves

Question 8

coefficient of friction

Answer 8

roughness between surfaces
μ

Question 8

banked car min/max speed (forces)

Answer 8

min - friction acts outwards
max - friction acts inwards

Question 9

conservation of mechanical energy (pendulums)

Answer 9

if stops at top mgh = KE
if keeps going 1/mu^2 > 1/2mv^2 + mgh

Question 9

gain in PE

Answer 9

mgl(1-cosθ)

Question 9

force out a rod vs in a rod

Answer 9

out = tension
in = thrust

Question 10

doing a loop attached to a string vs to a rod

Answer 10

string to have a full loop round tension has to be >0 as well as 1/mu^2 > 1/2mv^2 + mgh

Question 11

how to convert w into time taken

Answer 11

2pi / w = time taken
rad/ (rad/sec) = sec