Download Uniform Circular Motion

Uniform Circular Motion
Uniform circular motion is
the motion of an object
traveling at a constant
(uniform) speed in a circular
path.
Does an acceleration exist if
a particle is undergoing
uniform circular motion? Why
or why not?
Changing Velocity in
Uniform Circular Motion
The change in the velocity
vector is due to the change
in direction.
The direction of the change
in velocity is toward the
center of the circle.
The vector diagram shows:
vf = vi + Dv
Centripetal Acceleration
Magnitude ac of the centripetal acceleration
depends on the speed v of the object and the
radius r of the circular path. ac=v2/r
The acceleration always points toward the center
of the circle of motion.
The acceleration is always perpendicular to the
path of the motion.
Derivation of Centripetal
Acceleration
Centripetal Force
“Center-seeking” Force
Formula?
Period
Period, T, is defined as the time interval required
for one complete revolution of the particle.
Formula?
Angular
Speed/Translational
Speed
Quick Check
A particle moves in a circular path of radius, r, with speed,
v. It then increases its speed to 2v while traveling along
the same path. The centripetal acceleration of the particle
has changed by what factor?
0.25
0.5
2
4
From the same choices above, by what factor has the
period changed?
Example 1
What is the centripetal acceleration of the Earth
as it moves in its orbit around the Sun?
Example 2
A skater moves with 15 m/s in a circle of radius
30m. The ice exerts a central force of 450 N.
What is the mass of the skater?
Tangential and Radial
Acceleration
As a particle moves along a curved path, the direction of the total
acceleration vector, a, changes from point to point. At any instant
we can resolve it into components.
What are these components called?
Total Acceleration
The tangential acceleration
causes the change in the
speed of the particle.
The radial acceleration
comes from a change in the
direction of the velocity
vector.
The tangential acceleration:
at =
dv
dt
The radial acceleration:
v2
ar = -aC = r
The total acceleration:
Magnitude
a = ar2 + at2
Direction
Same as velocity vector if v is
increasing, opposite if v is decreasing
Example 3
A car leaves a stop sign and exhibits a constant
acceleration of 0.300 m/s2 parallel to the
roadway. The car passes over a rise in the
roadway such that the top of the rise is shaped
like an arc of a circle of radius 500 m. At the
moment the car is at the top of the rise, its
velocity vector is horizontal and has a magnitude
of 6.00 m/s. What are the magnitude and
direction of the total acceleration vector for the
car at this instant?
Quick Check
A particle moves along a path, and its speed increases
with time. In which of the following cases are its
acceleration and velocity vectors parallel?
When the path is circular
When the path is straight
When the path is a parabola
Never
From the same choices above, in which cases are its
acclereation and velocity vectors perpendicular
everywhere along the path?
Homework Problem
An athlete rotates a 1.00 kg discus along a
circular path of radius 1.06 m. The maximum
speed of the discus is 20.0 m/s. Determine the
magnitude of the maximum radial acceleration
of the discus.