Download Uniform Circular Motion

Circular Motion
Chapter 7.3
Motion & Forces
• What you already know:
– Velocity – a measure of the change in
over
with
.
– Mass – A measure of the amount of
an object
contains.
– Acceleration – A measure of the change in
over change in
.
– Force – A
or
that is equal to the mass
of the object multiplied by its acceleration (F = _____).
Uniform Circular Motion
• Uniform circular motion is defined by any object that
is moving at
in a circular path.
– Determining
:
» The distance an object moving in a circular path is
equal to the
(__ = _____).
» The time it takes an object to
complete one revolution is called
the
(___).
» It then follows that the speed of
an object moving in a circular path
can be determined by:
v=
Uniform Circular Motion
• If an object is moving at constant speed in a
circular path, can it be accelerating?
–
» Although the speed may be
,
the
is
.
v
» If
is changing over time,
then the
must be changing.
»
is the change in
over
(___ = ___).
» If the
is changing over time,
then the object must be
. v
v
v
Circular Motion – Instantaneous
Velocity
• Note that the
vector is at
the
vector and
at any given point along the circle.
to
to the circle
v2
r2

r1
r2

r1
r
v1
v = r/t
Circular Motion – Centripetal
Acceleration (ac)
• The
of an object moving in a circular path
always __________ ____________ _____ __________ ___
____ ___________, and is perpendicular to the velocity vector.
v2
-v1

v2
v
a
r
v1
v
a = v/ t
Centripetal Acceleration
• The angle between r1 and r2 is the same as the angle
between v1 and v2.
– Therefore, the triangles these vectors make are
such that:
=
– If you divide both sides by ___:
=
– Where :
»
= v and
=a
– Hence:
=
and
=
Centripetal Acceleration
• An alternative representation for centripetal
acceleration can be derived using the
and period of
.
»d=
»v=
– Substituting into ac =
» ac =
» ac =
Circular Motion –
Force
• To make an object move in a circular path, an
must act
or at right
angles to its
of
.
• This force is called
.
direction of velocity
Direction of
required to make object
move in a circular path
(
)
Centripetal Force
• Centripetal force is affected by:
– The
– The
– The
of the object (___).
of the object around the circle (___).
of the circle (___).
• Using Newton’s 2nd Law of Motion (Fc = mac),
centripetal force is mathematically represented as
follows:
Fc
Fc 
Note: Centripetal force is an
“
” force
How the Factors Affect
Centripetal Motion
• Which graph shows the proper
relationship with respect to force:
– Force vs. Mass.
Speed
– Force vs. Speed.
Radius
– Force vs. Radius.
Mass
Objects that travel in circular paths.
What is the cause of the force?
• The Earth – Sun System:
–
.
• A racecar traveling around a turn on the
racetrack:
–
.
• An athlete throwing the hammer:
–
.
The path of objects.
• If the centripetal force were suddenly removed
from an object moving in a circular path, what
trajectory (or path) would it follow?
Which Path?
(a)
(b)
(c)
Which Path?
•Why does the object travel in a straight path
once the centripetal force is gone?
– Because of
– An object in
wants
to
in
at
in a
.
– If the
is removed, the object will continue
in a straight path.
Example #1:
• A 1.5 kg cart moves in a circular path of 1.3
meter radius at a constant speed of 2.0 m/s.
– Determine the magnitude of the centripetal
acceleration.
– Determine the magnitude of the centripetal
force.
– Determine the period.
Example #1: (cont.)
• Centripetal Acceleration:
ac =
• Centripetal Force:
Fc =
• Period:
T=