Download Centripetal Force

Circular Motion A Review
• When we see an object carrying
out circular motion, we know that
there must be force acting on the
object, directed towards the
center of the circle.
• When you look at the circular
motion of a ball attached to a
string, the force is provided by
the tension in the string.
• When the force responsible for
the circular motion disappears,
e.g. by cutting the string, the
motion will become linear.
Going round in circles
• Speed may be constant
• But direction is continually
changing
• Therefore velocity is
continually changing
• Hence acceleration takes
place
Centripetal Acceleration
• Change in velocity is
towards the centre
• Therefore the
acceleration is
towards the centre
• This is called
centripetal
acceleration
Centripetal Force
• Acceleration is caused by
Force (F=ma)
• Force must be in the same
direction as acceleration
• Centripetal Force acts
towards the centre of the
circle
• CPforce is provided by
some external force – eg
friction
Examples of Centripetal Force
• Friction
• Tension in
string
• Gravitational
pull
Centripetal Force 2
What provides the cpforce in each case ?
Centripetal force 3
Circular Motion Calculations
• Centripetal
acceleration
• Centripetal
force
Period and Frequency
• The Period (T) of a body travelling in a circle at
constant speed is time taken to complete one
revolution - measured in seconds
• Frequency (f) is the number of revolutions per
second – measured in Hz
T=1/f
f=1/T
Angles in circular motion
• Radians are units of angle
• An angle in radians
=
arc length / radius
• 1 radian is just over 57º
• There are 2π = 6.28
radians in a whole circle
Angular speed
T = 2π/ω = 1/f
f = ω/2π
• Angular speed ω is the
angle turned through per
second
• ω = θ/t = 2π / T
• 2π = whole circle angle
• T = time to complete
one revolution
Force and Acceleration
•
•
•
•
v = 2π r / T and
T = 2π / ω
v=rω
a = v² / r = centripetal acceleration
a = (r ω)² / r = r ω² is the alternative
equation for centripetal acceleration
• F = m r ω² is centripetal force
Circular Motion under gravity
• Loop the loop is
possible if the track
provides part of the
cpforce at the top
of the loop ( ST )
• The rest of the
cpforce is provided
by the weight of
the rider
Weightlessness
• True lack of weight can only
occur at huge distances
from any other mass
• Apparent weightlessness
occurs during freefall where
all parts of you body are
accelerating at the same
rate
Weightlessness
These astronauts are in freefall
Red Arrows pilots
experience up to 9g (90m/s²)
This rollercoaster produces
accelerations up to 4g (40m/s²)
Circular Motion
By Farahin
Choudhury and
Summaiya
Rehman
•
•
•
•
Axis: the straight line around which rotation takes place.
Rotation: when an object turns about an internal axis.
Revolution: when an objects turns about an external axis.
Linear speed: the distance moved per unit time. It is greater on the
outer edge of a rotating object than it is closer to the axis.
• Tangential speed: speed of something moving along a circular path,
since the direction of motion is always tangent to the circle. It depends
on rotational speed and the distance from the axis of rotation.
• Rotational speed: the number of rotations per unit of time. The
rotational speed is always the same for all the objects, regardless of
where they are located.
• Centripetal Force: any force that causes an object to follow a
circular path. Centripetal means "center-seeking" or
Real Life Examples
• A merry-go-round rotates around its axis.
The people sitting in the merry-go-round
revolve around the same axis. The person
sitting towards the outer edge of the merry-goround has greater tangential speed than the
person sitting towards the middle. Everyone on
• As the string unwinds, the yo-yo rolls down
one side of the string. It then rolls back up the
other side of the string, while simultaneously
causing the string to wind up again
• The potential energy of the yo-yo at the top of
its motion is converted to rotational kinetic
energy as it falls, and then back to
gravitational potential energy again as it rises
• The velocity at the end of the string is
tangential to the orbit, that is, horizontal
Real life example: the YO-YO
• Average (Linear) Speed=2r/T r=radius and
T=period (also called Tangential speed)
• Centripetal Acceleration=v^2/r v=velocity and
r=radius
• Net Force=ma m=mass and a=acceleration
(this is Newton’s 2nd Law)
• Centripetal Force=mv^2/r m=mass,
v=velocity, and r=radius
• T=1/f and f=1/T f=frequency and T=period
A short Demonstration…
• http://www.youtube.com/watch?v=L6kn2tB-9E
Sample Word Problem
A small patch on a tire is located 20
centimeters from its axis of rotation.
If it makes 1 revolution in 12
seconds, what are its tangential and
rotational speeds?
(Hint: USE THE EQUATIONS!!!!!)
• Axis: the straight line around which
rotation takes place
• Rotation: when an object rotates around
an internal axis
• Revolution: when an object turns around
an external axis
• http--vip.vast.org-Circ_Lab-flashScrambler.swf
• Linear Speed: is the distance moved per
unit of time (points on the outside of the
circle travel further than points near the
axis)
• Rotational Speed: is the # of rotations
per unit of time (all parts on a circle rotate
in the same amount of time); “RPM”
» Linear Speed = radial distance x rotational speed
• On a merry-go-round the horses on the outer rail
are located 4 times as far from the horses on the
inside rail. If a girl sits on a horse on the inside rail
at a rotational speed of 3 RPM and a linear speed
of 4 m/s, what will be the rotational speed and
linear speed of her brother who is on a horse on the
outer rail?
L speed = rad distance x rot speed
=4x3
= 12 m/s
His rotational speed is the same at 3 RPM. His
linear speed however is a quicker 12 m/s.
• Centripetal Force is any force that causes
an object to follow a circular path.
• Gravitational and electrical forces act across
empty space as centripetal forces.
• Ex: A gravitational force directed towards the
center of the earth holds the moon in circular
orbit around the earth.
• Ex: Electrons revolving around the nucleus
of an atom are held in orbit by an electrical
force.
http--vip.vast.org-Circ_Lab-flash-Time%20shaft.swf