Circular Motion

1
Circular Motion

• Pearson 2007-2008

2
Uniform Circular Motion

• An object moving in a circle with constant speed,
  v, experiences a centripetal acceleration with
• a magnitude that is constant in time and
• is equal to
• a direction that changes
• continuously in time and
• always points toward the
• center of the circular path

For uniform circular motion, the velocity is
tangential to the circle and perpendicular to the
acceleration
3
Period and Frequency

• A circular motion is described in terms of the
  period T, which is the time for an object to
  complete one revolution.

The distance traveled in one revolution is
The frequency, f, counts the number of
revolutions per unit time.
4
Example of Uniform Circular Motion

• The moons nearly circular orbit about the earth
  has a radius of about 384,000 km and a period T
  of 27.3 days. Determine the acceleration of the
  Moon towards the Earth.

5
Moon...
So we find that amoon / g 0.000278 Newton
noticed that RE2 / R2 0.000273 This
inspired him to propose that Fgravity ? 1 / R2
(more on gravity in future lectures)
6
Uniform Circular Motion
motion in a circle or circular arc at constant
speed
the acceleration changes the direction of the
velocity, not the magnitude
the center-seeking or centripetal acceleration
is always orthogonal to the velocity and has
magnitude
The period of the motion
7
Uniform Circular Motion
Newtons 2nd Law The net force on a body is
equal to the product of the mass of the body and
the acceleration of the body.
The centripetal acceleration is caused by a
centripetal force that is directed towards the
center of the circle.
8
Demo 1D-5
Does the contact force between the wine glass and
red-water remain constant in uniform circular
motion?
9

• Consider the glass directly overhead. Choose the
  correct statement
• The water doesnt fall because the centripetal
  force on the water cancels the force of gravity.
• The water doesnt fall because there isnt enough
  time for it to fall.
• The water doesnt fall because of the horizontal
  force applied to it by the glass, plus friction
  with the glass.
• The water is falling, but the glass is falling
  faster than it would under free fall.

10
mac mv2/r mg Ny or ac g ? N/m
When N0, the centripetal acceleration is just g.
11
Top
Bottom
12
Top
What speed is needed to lose contact between wine
glass and red-water?
13

• 2) A person riding a Ferris Wheel moves through
  positions at (1) the top, (2) the bottom and (3)
  midheight. If the wheel rotates at a constant
  rate, rank (greatest first) these three
  positions according to...
• the magnitude of persons centripetal acceleration
  
• 2,1,3
• 1,2,3
• 3,2,1
• all tie
• The magnitude of the Normal force?

14

• (b) the magnitude of the net centripetal force on
  the person
• 1,2,3
• 3,1,2
• 3,2,1
• all tie

• (c) the magnitude of the normal force on the
  person
• all tie
• 2,3,1
• 3,2,1
• 1,2,3

15
Demo 1D-2 Conical Pendulum
q
H
R
The period, T, is independent of mass and depends
only on H.
16
A car of mass, m, is traveling at a constant
speed, v, along a flat, circular road of radius,
R. Find the minimum µs required that will
prevent the car from slipping
17
A mass, m, on a frictionless table is attached to
a hanging mass, M, by a cord through a hole in
the table. Find the speed with which m must move
in order for M to stay at rest.
18
A car of mass, m, is traveling at a constant
speed, v, along a curve that is now banked and
has a radius, R. What bank angle, q, makes
reliance on friction unnecessary?
frictionless
q
19
An airplane is flying in a horizontal circle with
a speed of 480 km/hr. If the wings of the plane
are tilted 40o to the horizontal, what is the
radius of the circle in which the plane is
flying? (Assume that the required force is
provided entirely by an aerodynamic lift that
is perpendicular to the wing surface.)
v480 km/hr
L
L
W