Embedded Files
The students can evaluate the evidence provided by data sets in relation to a particular scientific question.
The acceleration of the center of mass of a system is related to the net force exerted on the system.
Evaluate, using given data, whether all the forces on a system or whether all the parts of a system have been identified.
The acceleration is equal to the rate of change of velocity with time, and velocity is equal to the rate of change of position with time.
a. The acceleration of the center of mass of a system is directly proportional to the net force exerted on it by all objects interacting with the system and inversely proportional to the mass of the system.
b. Force and acceleration are both vectors, with acceleration in the same direction as the net force.
c. The acceleration of the center of mass of a system is equal to the rate of change of the center of mass velocity with time, and the center of mass velocity is equal to the rate of change of position of the center of mass with time.
d. The variables x, v, and a all refer to the center-of-mass quantities.
Essential Equations:
Intro to Circular Motion
Intro to Circular Motion
Activities:
Activities:
Push it into a circle:
Using a string and mass, move the mass in a perfect circle.
OUTLINE the method necessary to move the mass in a circle?
Toy train:
How does changing the radius change the tension in the spring?
Sketch a graph of Tension v. Radius
Conic Pendulum:
How does the angle θ change as the speed increases?
How fast would the mass need to be spinning for θ to equal 0˚?
Cresting a Hill - Hill Scenarios
What is the maximum velocity a car can travel before leaving the ground (when does a hill become a ramp)?
Looping Bucket of Water:
Describe the changes in tension in string as the bucket spins in a vertical circle.
Earth-Sun System:
How do the planets stay in the solar system?
Dua Lipa's Spin - Physical video
The coolest video since MJ's Smooth Criminal Lean
Objectives
For each of the activities on the left:
Sketch the setup.
Label possible quantities to measure.
Draw FBDs with ON...BY...notation
Sketch graphs of possible relationships.
Introduce the quantities of circular motion,
Understand that if a body moves in a circle there must be an acceleration towards the centre and therefore an unbalanced force towards the centre.
The Spin at ~2:20 into the video.
Angular v. Tangential Velocity
Angular v. Tangential Velocity
Photo: 1/20 sec. off center.
How fast are the lights moving? - Relative speeds, tangential speed v. angular velocity.
What information do you need to know?
Using the strings of lights, your phone and Geogebra, can you find the tangential speed of the LED?
The photo of the Ferris Wheel was a 2.5s exposure. How fast are the people moving in the baskets/seats?
Geogebra Analysis
2.5s exposure, estimate the velocity of the passengers on the outer edge of the wheel. The Ferris wheel has a diameter of 30m.
Ferris Wheel from: Parque da Cidade Sarah Kubitschek, Brasilia - Federal District, Brazil
Core Terminology
Core Terminology
Period, frequency, angular displacement and angular velocity
An object that moves in a circle at constant speed is said to be undergoing uniform circular motion. Period and frequency for circular motion are defined as follows:
Period (T ) = the time for an object to complete one rotation (360º or 2π rad)
Frequency (f ) - the number of rotations in a given time (usually one second)
Period and frequency are connected by the equation,
f=1/T
In the diagram to the right an object with speed v is moving along the arc of a circle of radius r through and angle θ.
These are defined as follows:
Radius (r ) = distance between rotating object and the centre of rotation
Speed (v ) = speed of rotation around the circumference of the motion
Angular displacement (θ ) - the angle through which the object has rotated from a fixed reference point, in radians (rad)
The radian (rad) is a more useful unit, compared to degrees (°), because it is based on a natural phenomena - the arc of a circle with the same length as its radius has an angle of one radian.
Angular velocity (ω ) = angle swept out per unit time (rad s-1)
This can be stated as an equation, to the right.
Derivation of Centripetal Acceleration Formula (Calculus is involved)
Derivation of Centripetal Acceleration Formula (Calculus is involved)
Consider two objects rotating with uniform circular motion as shown in the GeoGebra simulation below, by Ken Schwartz. Check the Animate box and then use slider a or b to change the radius of one of the circles.
Uniform Circular Motion
A model of the spinning force sensor:
Sample Tangential Speed Problems:
Sample Tangential Speed Problems:
The International Space Station orbits the Earth at an average height of 400 km, above the surface of the earth, the Space Station orbits the Earth every 90 minuets. Using the current data from the ISS (follow the link to the right), the radius of the Earth is rearth = 6.37 x 106m.
Determine the velocity of this satellite in the units of m/s. 27536km/h = 7648.8 m/s
Determine the time for the ISS to orbit the Earth. @27536km/h & 437km = 5591s
Calculate the current centripetal acceleration of the ISS. @27536 km/h &437 km = 8.59 m/s2
A geosynchronous satellite is a satellite that orbits the earth with an orbital period of 24 hours, thus matching the period of the earth's rotational motion. A special class of geosynchronous satellites is a geostationary satellite. A geostationary satellite orbits the earth in 24 hours along an orbital path that is parallel to an imaginary plane drawn through the Earth's equator. Such a satellite appears permanently fixed above the same location on the Earth. The altitude of a geosynchronous satellite is 3.59x107m.
If a geostationary satellite wishes to orbit the earth in 24 hours (86400 s), determine the velocity of the satellite in m/s? (Given: MEarth=5.98x1024 kg, rEarth = 6.37 x 106m) v = 3073 m/s
Determine the centripetal acceleration of the geostationary satellite. a = 0.22 m/s2
Circular Velocities and Centripetal Accelerations TSPs
Circular Velocities and Centripetal Accelerations TSPs
Horizontal Centripetal Forces
Horizontal Centripetal Forces
ACTIVITIES:
ACTIVITIES:
Which way is the acceleration? (In Class activity)
Using a CORK FLOAT ACCELEROMETER, describe the motion of the cork when the accelerometer is accelerating.
Hold the accelerometer at an arm's length in front of you and watch the movement of the cork as you:
walk forward, (constant speed and accelerating)
walk backwards (constant speed and accelerating) and
spin around in a circle.
Tension in the spring (Problem Set) - Solutions
How does this relate to the string and mass activity?
Where is the accelerometer in your phone?
Using the accelerometer in your phone or force/acceleration sensor, determine the location of the sensor within the phone.
How does this relate to the string and mass activity?
Horizontal Circle Problems:
Check your Understanding:
Circular Motion FA 1 - Concepts of Circular Motion - Self Graded
Circular Motion FA #2 - Forces on a Plane - Solutions
Circular Motion FA #3 - Masses on a Turntable - Solutions
American Eagle Front Seat POV 2015 FULL HD Six Flags Great America
The American Eagle Roller Coaster - Six Flags Great America - Chicago, Il
Horizontal to Vertical Circles
Horizontal to Vertical Circles
ACTIVITIES:
ACTIVITIES:
Moving from horizontal to vertical.
Tension in String while moving as a pendulum.
Identify the changes in forces as a rotating object moves from a horizontal plane to a vertical plane.
Describe the forces at the 'top' and 'bottom' of the loop.
Objectives:
Understand that if a body moves in a circle there must be an acceleration towards the centre and therefore an unbalanced force towards the centre.
Identify the centripetal force in a variety of examples.
Looping the Loop
Horizontal v. Vertical Circles - Wireless Force Sensors - Vernier Graphical Analysis
How do the centripetal forces change between horizontal and vertical circles?
Tension at bottom of a pendulum, suppose a mass is hung from a string. The tension in the string is a constant 5-N. The mass is then pulled to the side and allowed to swing, compare the tension in the string at the bottom of the arc to the original 5-N.
By swinging the sensor into a full VERTICAL circle, describe how the forces change at various parts of the circle.
How does the Tension in the string change through the circle? Vertical Circle - Looping Problems:
Flipping Physics Video Resources:
Khan Academy Loop de Loop Problem
Khan Academy - Video Intro
Vertical Loop Problems
American Eagle Hills Set 2
Problem Set 3 (Q10) - Solutions
In the diagram above, the T (tension in the string) can be considered the limiting factor in the motion of the object.
At the BOTTOM of the circle the tension limits the maximum velocity the object can travel, as the weight of the object and the centripetal force are added together.
At the TOP of the circle the tension limits the minimum velocity the object can travel and maintain a circular path. If the tension is negative (mg is greater than the FC) then the object will 'fall out of the circle'.
In a rollercoaster the Tension is also considered the Normal force.
Running to the MAX....Pepsi Max (Running in a loop)
Objectives:
Introduce the quantities of circular motion, (angular velocity)
Identify the centripetal force in a variety of examples. - Looping Problems
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