Transcript Circular Motion - science

Circular Motion
Objectives
Students should be able to:
(a) define the radian;
(b) convert angles from degrees
into radians and vice versa;
Outcomes
• All should
• Be able to define the radian.
• Be able to convert degrees into radians and
vice-versa.
• Most Should
• Be able to understand the reasons for using
radians.
• Be able to solve problems involving a mixture of
degrees and radians.
• Some Could
• Be able to explain what the idea of centrifugal
force is and why it is imaginary.
• Be able to derive the equations for circular
speed and centripetal acceleration.
Rotational Kinematics
How do we
describe an
object moving in
a circle?
Centripetal Force
• A circle follows a curve all the way round
and we can describe it quantitatively as
well as qualitatively.
• All objects that follow a curved path must
have force acting towards the centre of
that curve.
• We call this force the centripetal force.
(Greek: Centre seeking).
Centripetal acceleration
• Since velocity is speed in a given direction
if an object is travelling at a constant
speed but is constantly changing direction
it must be accelerating.
• This is what is happening in circular
motion.
• The acceleration is called Centripetal
Acceleration.
Dynamics of Rotation
Examine circular
motion taking
Newton’s Laws into
consideration.
1st Law2nd Law3rd Law-
Dynamics of Rotation
1st Law
• Is Moon at rest?
MOON
• Is Moon moving in a
straight line?
EARTH
• Conclusion
Dynamics of Rotation
1st Law
Objects executing
circular motion have
a net force acting on
them…even if you
can’t see the agent
of the force.
What force acts on the
Moon?
MOON
EARTH
• Earth and Moon orbit
the centre of mass of
the system.
• Located 1070 miles
below the Earth’s
surface or 2880
miles from centre of
Earth.
Circular velocity
• The instantaneous linear velocity at a point in
the circle is usually given the letter v and
measured in metres per second (m s-1).
• Speed is defined as the distance / time.
•
• For a circle, 1 complete circumference is 2pr and
T is the Time period for one rotation (T)
• So
v = 2pr / T
v
v
Q
O
q
P
a = v2/r
a is the Centripetal Acceleration. The change in
velocity.
Outcomes
• All should
• Be able to define the radian.
• Be able to convert degrees into radians and
vice-versa.
• Most Should
• Be able to understand the reasons for using
radians.
• Be able to solve problems involving a mixture of
degrees and radians.
• Some Could
• Be able to explain what the idea of centrifugal
force is and why it is imaginary.
• Be able to derive the equations for circular
speed and centripetal acceleration.