Download (CON)CircularMotion

CIRCULAR
MOTION
Mr.
Theuerkauf
CIRCULAR NOTES

Axis – the line or point around
which an object rotates.

Rotation: spinning around an
internal axis


Example: The Earth rotates around
its axis once every 24 hours (1 day).
Revolution: Moving around an
external axis

Example: The Earth revolves
around the sun once every 365.25
days (1 year).

MORE ABOUT CIRCULAR MOTION

Period – the amount of time it takes for ONE
rotation or revolution.
2r C
v

T
T
Unit: seconds (s)
 Frequency – the number of rotations or
revolutions per second.
Unit: Hertz (Hz)
# revolutions(rotations)

f

#seconds
Period and frequency are inverse (reciprocals).
1
T 
f
1
f 
T
LINEAR VELOCITY
Linear Velocity – the distance
moved per unit time




Always drawn tangent to the circular
path.
Direction is the direction the object
wants to move (inertia – wants to
move in a straight line)
Distance = circumference (C)
C = 2πr
Time = time for one revolution = Period (T)
Tangential Velocity depends on how far
away the object is from the center of
the circle (radius)
At the center, v = 0 m/s b/c r = 0
As you move away from the center,
radius increases so your tangential
velocity increases
2r C
v

T
T
ROTATIONAL VELOCITY

Rotational Velocity – the number of rotations per
unit time
Depends on the number of degrees you turn in a
given amount of time
 Does NOT depend on where you stand (radius)
because the distance traveled (angle) will be the same
 DIRECTLY proportional to tangential velocity.


The faster the object turns (rotational velocity) the fater the
tangential velocity will be.
CENTRIPETAL ACCELERATION
When an object moves in a circle, direction is
constantly changing. Therefore, the velocity is
constantly changing. The object is
ACCELERATING.
 Centripetal Acceleration – the acceleration due to
an object moving in a circular path; constantly
changing velocity

v2
ac 
r
Unit: m/s2
 Direction is always towards the center of the
circle

CENTRIPETAL FORCE – THE NET
FORCE CAUSING CIRCULAR
MOTION
mv
Fc  Fnet  mac 
r
2
Units: N
Direction of Fc is always into the center of the
circle; like ac.
Fc is not an additional force; it is just the net force
that is causing the object to keep changing
direction.
Examples: tension in a string, the wall of a salad
spinner.
If Fc is removed, the object will fly off in the
direction of the tangential velocity (straight line).
TORQUE

A net torque produces ROTATION
Torque (τ): The ability of a force to cause an object to
rotate. More torque means the object will rotate
more easily.
 Axis of rotation: the invisible line around which an
object rotates. Examples: your elbow, the hinge of a
door.

TORQUE DEPENDS ON…
1. The amount of force exerted
2. The distance between the force and the axis of
rotation
Lever Arm – the distance between the applied
force and the axis; measured in meters.
Example: Using a wrench. Hold close to
bolt, it’s harder to turn than when you hold
farther away. Greater lever arm, greater
torque, easier to turn.
3. The angle that the force is applied.
Perpendicular is best.