Transcript Intro to Circular Motion

INTRO TO CIRCULAR MOTION
‘Round and ‘round we go!
OBJECTIVES
Define & understand the following terms: period,
frequency, angular displacement & angular
velocity
 Understand and calculate centripetal force and
acceleration
 Identify the forces providing the centripetal force
(tension, friction, gravitational, electrical &
magnetic)
 Qualitatively & quantitatively describe examples
of circular motion including cases of vertical &
horizontal circular motion

ENGAGE & EXPLORE
Hold the string and swing the ball around your
head. Release when you believe the ball will hit
the target. You have 3 opportunities to hit the
target.
 Relay-race: get into teams of 3-4. When the first
person hits the target, hand the ball off to the
next team mate. The fastest group to get
everyone to hit the target and sit down picks
from the prize bucket.

ANALYSIS
When you hit the target, where was the ball in
it’s circular path when you let it go?
 What forces/properties of matter guided the ball’s
motion once you let go?
 What does this mean about the direction of the
ball’s velocity when you let it go? Draw a picture
to illustrate your idea.

EXPLAIN:
IMPORTANT NEW SYMBOLS & VOCABULARY
Arc length – s – distance travelled in an arc
 Radius – r- the distance from the center to the
perimeter of the circular path



Angle – θ – the angle subtended 𝜃 =

units: radians
Angular velocity – ω – the rate of change of the angle
𝑣
∆𝜃
𝜔 = = = 2𝜋𝑓
𝑟

𝑠
;
𝑟
∆𝑡
Linear velocity – v – rate of displacement 𝑣 =
∆𝑥
∆𝑡
Angular Acceleration – α – rate of change of the
𝑎𝑡
∆𝜔
angular velocity 𝛼 = =
𝑟
∆𝑡
= 𝜔𝑟
EXPLAIN:
IMPORTANT NEW SYMBOLS & VOCABULARY


Frequency – f – number of complete revolutions per
second; units: 𝑠 −1 = 𝐻𝑧
Period – T – the amount of time required for one
1
complete revolution 𝑇 =
𝑓
ELABORATE
Create 8 vocab tabs using the single sheet of paper
as directed
 Outside: symbol


Inside: definition, equation & picture
Use colors! This is homework if not finished by
the end of class.
IB EXPLAIN: FRAME OF REFERENCE

Inertial frame of reference – what we’ve been
exploring
Forces obey newton’s laws
 a frame of reference in which a body remains at rest or
moves with constant linear velocity unless acted upon
by net external forces
 Example: everything we’ve done so far


Rotating frame of reference (non-inertial)
If your frame of reference has a non-uniform, or
accelerated motion, then the Law of Inertia will appear
to be wrong, and you must be in a non-inertial frame of
reference.
 Performing an experiment on an accelerating train

ELABORATE: EXAMPLES CALCULATIONS
USING ANGULAR SPEED
Calculate the angular speed of the second hand
on a clock.
 Calculate the angular speed of the minute hand
on a clock.
 A car drives round a circular track of radius 1.0
km at a constant speed of 26 ms-1. What is the
angular speed?
 A disc rotates at an angular speed of 4.7 rad s-1.
An object is placed a distance of 4.0 cm from the
center, what is it’s linear speed?

EVALUATE: YOU TRY!
Calculate the angular speed of a 4000 rpm
(rotations per minute) CD Rom drive.
 Calculate the angular speed of the hour hand on
a clock.
 A disc rotates at an angular speed of 4.7 rad s-1.
An object is place a distance of 8.0 cm from the
center, what is it’s linear speed?
 Compare the answer to the last problems with
that of the last example. What happens to the
linear speed of an object as it moves outward at
the same angular velocity? Why do you think this
is?

EXPLAIN: WHAT MAKES THINGS MOVE IN
CIRCLES?
Video: Circular Motion
Velocity is speed in a direction
 In circular motion, direction is changing (even if
speed is constant), so the velocity is changing
which means that the object is accelerating –
Centripetal acceleration ac



𝑎𝑐 =
𝑣2
𝑟
=
4𝜋2 𝑟
𝑇2
Accelerations are caused by net forces, so there
must be a net force acting on the object –
Centripetal force Fc


Directed inward – center-seeking
𝐹𝑐 =
𝑚𝑣 2
𝑟
= 𝑚𝜔2 𝑟
ELABORATE: EXAMPLES
EVALUATE: YOU TRY!

The speeds of a 600-kg roller coaster car at the
top of three consecutive hills are shown below.
The radii of the hills are shown. Determine the
acceleration of and net force and normal
force experienced by the car at the top of each
hill.
EXPLAIN – EQUATIONS OF ROTATIONAL
MOTION
We can use rotational analogs of the linear
equations we already know to solve for unknown
quantities, just like we did before.
Equations for constant
angular acceleration
Equations for constant
linear acceleration
𝜃
= 𝜔𝑎𝑣𝑔 𝑡
𝑥
= 𝑣𝑎𝑣𝑔 𝑡
𝜔
= 𝜔0 + 𝛼𝑡
𝑣
= 𝑣0 + 𝑎𝑡
 ∆𝜃
=
2
=
𝜔
1
𝜔0 𝑡 + 𝛼𝑡 2
2
𝜔0 2 + 2𝛼∆𝜃
1
2
 ∆𝑥 = 𝑣0 𝑡 + 𝑎𝑡
2
2
2
 𝑣 = 𝑣0 + 2𝑎∆𝑥
Can you see the similarities?
EXTEND
International mindedness: International
collaboration is needed in establishing effective
rocket launch sites to benefit space programs.
 TOK: Foucault’s Pendulum – simple, observable
proof of the Earth’s rotation
 Use: Playground/amusement park rides

PRACTICE

Try to get 100 points on the kinetic books
assignment. You may work with a partner.