PHYSICS UNIT 3: CIRCULAR
& ROTATIONAL MOTION
CIRCULAR MOTION

Uniform Circular Motion



period, T: time for one complete
revolution, unit: s
speed is constant
 v = 2pr/T
(r: radius)
velocity is constantly
changing (because
direction is changing)
CIRCULAR MOTION

all turning
objects have
centripetal
(centerseeking)
acceleration
CIRCULAR MOTION

centripetal acceleration, ac = v2/r
the greater the speed, the greater the
centripetal acceleration
 the smaller the radius of the turn, the
greater the centripetal acceleration
 a centripetal acceleration requires a
centripetal force

CIRCULAR MOTION

no
centrip
etal
force =
no
turning
(linear
motion)
CIRCULAR MOTION

centripetal force, Fc = mv2/r
any force can be a
centripetal force:
gravity (planets &
moons), friction (car
turning a corner),
tension (ball on a
string), etc.
CIRCULAR MOTION

Frames of
Reference - inside
a turning object,
there seems to be a
centrifugal (centerfleeing) force pulling
on objects
CIRCULAR MOTION

Frames of
Reference - outside
the turning object,
we see objects
inside move in a
straight line
(inertia), until they
get pulled into the
turn by centripetal
force
CIRCULAR MOTION

centrifugal force
only exists within
the turning
object’s frame of
reference - it is a
fictitious force
CIRCULAR MOTION

Frames of
Reference things moving
on a rotating
object seem
to be made to
turn by the
“coriolis force”
PHYSICS
UNIT 3: CIRCULAR &
ROTATIONAL MOTION
QUIZ 3.1
A 50 kg child on a merry-go-round sits 2.0 m
from the center and makes 2.0 complete revolution
every second.
(a) Find the child's period.
(b) Find the child's tangential speed.
(c) Find the child's centripetal acceleration.
(d) Find the centripetal force on the child.
v = 2pr/T
ac = v2/r
Fc = mv2/r
PHYSICS
UNIT 3: CIRCULAR &
ROTATIONAL MOTION
UNIVERSAL GRAVITATION

Newton's Law of Universal Gravitation: masses
attract
 gravity force is proportional to each mass
 twice the mass = twice the force
 gravity force is inversely proportional to the
square of the distance between the masses
 twice the distance = ¼ the force

distance measured from center of mass:
point on a body around which mass is
UNIVERSAL GRAVITATION

Newton's Law of Universal Gravitation:
Fg = Gm1m2/r2
 FG: force of gravity, m: mass, r: distance
between masses
 G: universal gravitational constant,
6.67×10-11 Nm2/kg2
 gravity is only significant for very large
masses

UNIVERSAL GRAVITATION


acceleration due to gravity, g = Gme/r2
Also known as the gravitational field strength




me: earth's mass (5.97×1024 kg)
r: distance from earth’s center (6.38×106 m +
altitude)
g is only 9.80 m/s2 at sea level – it decreases as
altitude increases
g is different on other planets & moons (it
depends on the planet’s mass and radius)
UNIVERSAL GRAVITATION

Orbits: gravity provides the centripetal
force
stable orbit: Fc = Fg
 orbit speed v = √Gm /r
e
 orbit period T = 2pr/v
 geosynchronous orbit: T = 24.0 hrs,
satellite stays over same position on
earth

UNIVERSAL GRAVITATION

Orbits
always falling but never reaching the
ground
 "Weightlessness" is NOT gravity-less
 no gravity = no orbit
 weightless is no normal force

PHYSICS
UNIT 3: CIRCULAR &
ROTATIONAL MOTION
ROTATIONAL MOTION

Rotational Motion: rotation around an
internal axis
angle, q: how much an object has rotated,
unit: radian (rad)
 2p rad = 360º = 1 revolution (rev)
 angular velocity, w = Dq/t : rate of rotation,
unit: rad/s
 frequency: revolutions per second, unit:

ROTATIONAL MOTION


angular acceleration, a= Dw/t: rate of
change in rotation, unit: rad/s2
Rotational Motion & Circular Motion

for any point on a spinning object:
 v = rw
2
 a = rw
c
ROTATIONAL MOTION

torque, t: rotating effect
of a force, unit: Nm
t = Fdsinq
 d: "torque arm" or
"lever arm“
 q: angle between F
and d
 torque direction:

ROTATIONAL MOTION


Torque is zero when q = 0º or 180º
Torque is maximum when q = 90º
ROTATIONAL MOTION

Newton's Laws for Rotary Motion
A spinning object keeps spinning with
constant angular velocity unless a net
torque acts on it
 A net torque causes an angular
acceleration
 For every action torque, there is an equal
and opposite reaction torque

ROTATIONAL MOTION

Rotational Equilibrium: object is
balanced, or moves with constant
angular velocity, due to no net torque

Stc = Stcc
d1
F1
d2
F2
F2d2 = F1d1
PHYSICS
UNIT 3: CIRCULAR &
ROTATIONAL MOTION
UNIT 3 REVIEW
v = 2pr/T
ac = v2/r
Fc = mv2/r
Fg = Gm1m2/r2 G = 6.67×10-11 Nm2/kg2
g = Gmp/r2
v = √Gmp/r
me = 5.97×1024 kg
re =
6.38×106 m
w = Dq/t
a= Dw/t
v = rw
ac = rw2