Download circular motion

• CRSHS, III- Galileo,
Physics
Teacher: Mrs. Maria Ruth
Edradan
Group 4 task:
Catulay
powerpoint
Yee
laptop
Pomoy
info
Matildo
info
Bonono
info
Joaquino questions
Motion in a Circle
The rules of circular motion help us to describe:
• movement of a car going round a corner,
• a tethered model aeroplane;
• the planets in their orbits.
Angular Velocity
• The speed of a body moving in a circle can be
specified either by its speed along the tangent
at any instant (linear speed) or by the angular
velocity. This is the angle swept out in unit
time by the radius joining the body to the
centre. It is measured in [rad s-1].
Angular Acceleration
• Angular acceleration is the rate of
change of angular velocity over
time. In SI units, it is measured in
radians per second squared
(㎯，rad/s2), and is usually
denoted by the Greek letter alpha
(α).
Angular Acceleration
Mathematical definition
• The angular acceleration can be defined as
either:
• where ω is the angular velocity, aT is the linear
tangential acceleration, and r is the distance
from the origin of the coordinate system that
defines θ and ω to the point of interest.
Linear Acceleration
• The linear acceleration of a body is the rate of
change of linear velocity with time. It is a
vector.
• If acceleration is uniform the speed must be
increasing by equal amount in equal time
intervals.
CIRCULAR MOTION: introduction
In physics, circular motion is rotation along a circle: a
circular path or a circular orbit.
It can be uniform, that is, with constant angular rate of
rotation, or non-uniform, that is, with a changing rate
of rotation.
Circular motion is another simple type of motion. If an
object has constant speed but an acceleration always at
right angles to its velocity, it will travel in a circle. The
required acceleration is directed toward the center of
the circle and is called centripetal acceleration .
CIRCULAR
MOTION:
introduction
Uniform Circular
Motion
UNIFORM CIRCULAR MOTION
An object moves at a constant speed
along a circular path.
Uniform Circular Motion
• Uniform circular motion can be
described as the motion of an object in
a circle at a constant speed.
• As an object moves in a circle, it is
constantly changing its direction.
• At all instances, the object is moving
tangent to the circle. Since the
direction of the velocity vector is the
same as the direction of the object's
motion, the velocity vector is directed
tangent to the circle as well.
Speed Vs. Velocity
• If the speed is constant, will the
velocity be constant?
_______________________________
• Why is velocity not constant?
_______________________________
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Centripetal Acceleration
• In 1673, Christian Huygens was able to determine the following
relationship between ac, v and R.
• Changing velocity is acceleration. The acceleration of the object is
directed toward the center of the circle, and is of constant
magnitude a=v2/r, where r is the radius of the circle and v is the
speed of the object (with mass m). This type of acceleration is called
radial or centripetal acceleration.
• Radial acceleration results from the action of the force generated by
the string that pulls the ball toward the center of the circle. In the
case of a satellite in orbit, the force causing the radial acceleration is
Earth’s gravity pulling the satellite toward the center of the planet.
ac=V2 /R
Centripetal Acceleration
Acceleration can also involve a change in
the direction an object is moving
• A ball on the end of a string being whirled
overhead at a constant speed is an example
of this type of acceleration.
• Since velocity is a vector quantity like
acceleration, velocity has a speed
component (magnitude) and a direction
component.
• At every instant in its motion overhead, the
ball’s velocity is changing because the
velocity’s direction is different at every
point on the circular path.
• When a body goes around the circle of radius
r, it is just travelling around the circumference
of the circle, so it covers the entire distance
equivalent to 2∏r. Instead of using time, we
introduce a new term, called Period,
represented by the Greek letter tau (T)
So, velocity is equivalent
to the following formula:
Instead of measuring the time it takes to
complete one revolution, you could also
identify time in terms of the number of
revolution of cycle completed per unit time.
This term is called frequency, represented by
the letter f.
Frequency and Period are related by this
equation:
f=
1/
T
It can also be expressed in terms of
frequency:
v= 2∏rf
Expressing our centripetal acceleration in
terms of frequency:
∏
In terms of period:
∏