Circular Motion (M5)

Question 1

Critical velocity at the top of a roller-coaster

Answer 1

F = W + R
R = 0 so F = W
mvv/r = mg
vv = gr
v = rt(gr)
Minimum v to stay on

Question 2

Critical velocity on a humpback bridge

Answer 2

F = W - R
R = 0 so F = W
mvv/r = mg
vv = gr
v = rt(gr)
Maximum to stay on

Question 3

Critical velocity on a loop the loop

Answer 3

Start: GPE = mgh
Top of loop: GPE = 2mgr
KE = 0.5 mvv = 0.5 mgr
Total E at the top = 2mgr + 0.5mgr
Conservation of energy: mgh = 2.5mgr
h = 2.5r

Question 4

Pendulum circular motion

Answer 4

Th = Tsin¤
TV = Tcos¤

Vertically: Tcos¤ = mg
Horizontally: Tsin¤ = F = mvv/r

Tsin¤/Tcos¤ = mvv/r ÷ mg = vv/rg
tan¤ = vv/rg

If r is constant, ¤ up = v up
Fastest at ¤ = 90

If ¤ is constant, r upb= v up
vv directly proportional to r

Question 5

Angular velocity

Answer 5

The rate of change of angle for an object moving in a circular path.
W = 2pi/T
W = 2pi f

Question 6

Centripetal acceleration

Answer 6

The acceleration of any object travelling in a circular path at constant speed, which always acts towards the centre of the circle.

Question 7

Centripetal force

Answer 7

A force that keeps a body moving with a constant speed in a circular path.

Question 8

Whirling bung practical

Answer 8

Marker 20cm from bung.
Hang masses at end of string
Measure t for 10 revolutions, keeping marker at end of tube.
Calculate v with speed = distance / time and distance = circumference
Add masses and plot F against v^2
Gradient = m/r
Calculate mass from gradient and compare with actual value.