Unit 3 Circular and Energy
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PHYSICS 20 - STA NOTE BOOKLET
Unit 3 – Circular and Energy Chapter 5 – Circular Motion Name: ______5.1 – Defining Circular Motion 5.2 – Centripetal Acceleration 5.3 – Horizontal and Vertical Acceleration 5.4 – Satellites and Orbits 5.1 – Defining Circular Motion
Uniform Circular Motion
• An object moving at a constant velocity
Constant velocity means TWO things
1. Constant speed
2. Constant direction
• An object that is undergoing uniform circular motion is moving around a circle at a constant speed.
• But, any object moving in a circle is constantly changing direction . . . . so it cannot have a constant velocity.
So, for an object moving in a circle, the direction of the velocity is always tangent to the circle .
The diagram depicts an object (bob) moving in a clockwise circle. o if the “bob” (or in this case rock) is constantly changing direction, by definition it is ACCERLERATING (acceleration = any change in velocity) o if it wasn’t accelerating, it would be travelling in a straight line
o the Δv is towards the centre the acceleration is in this direction o called CENTRIPETAL ACCELERATION meaning ‘centre seeking’ o According to Newton’s 2nd Law, what is happening when something is ACCELERATING? o since acceleration is towards the centre, force must also be towards the centre called Centripetal Force Do not confuse CENTRIPETAL with CENTRIFUGAL! A person in a car going around a circle might say a ‘centrifugal force’ was pushing them across the seat and out of the circle. In fact, that’s just INERTIA! The car is trying to keep you in the circle, that’s CENTRIPETAL!
Centripetal Acceleration
o circular motion is also called periodic motion (periodically it gets back to where it started and keeps going)
o Two units of time are important in circular motion
Period
o time to go through one revolution
o “seconds per cycle”
o measured in seconds (s)
Frequency
o how often something repeats itself
o cycles per second
o measured in hertz (Hz) Example 1:
A pendulum swing at a frequency of 0.90 Hz. Calculate the period of the pendulum’s swing.
Example 2:
You are thinking of buying a new computer. One specification you are looking for is that the hard drive spins at 7200 rpm.
a) Explain what 7200 rpm means.
b) Determine the frequency in Hz.
c) Determine its period. Circular Motion
o objects travelling in a circle exhibit constant SPEED or Uniform Circular Motion
o formula for speed
o but our “d” is circumference
o creating…
o but… the time to complete one trip around the circle is called PERIOD and has the symbol T
o thus… Ex 1: What is the circular speed required if an object completes one orbit of a circle with a radius of 4.00 m in a time of 5.00 s?
Ex 2: Determine the length of a student’s arm if she can swing a pail around five times in a circle at 2.72 m/s in 7.5s.
Variation of formula if given frequency instead of T
so substitute
Ex 3: If an object travelling in a circle of 5 m radius has a frequency of 6 Hz, what is the circular speed of the object? 5.2 - Centripetal Acceleration
Centripetal Acceleration
o in order for VELOCITY to change there must be some acceleration
o Ex: What is centripetal acceleration of a student driving at 60 km/h in a traffic circle that is 120m across? Variation of the formula
o try deriving the formula using the alternative speed formula using frequency Ex: What is the centripetal acceleration of a horse running around a track with a radius of 37 metres, once every 12 s?
Ex: What is centripetal acceleration of a stone being whirled in a circle at the end of 1.75 m string with a frequency of 2.25 Hz?
Centripetal Force
o like all acceleration, F=ma, in this case
o Using our three different formulas for ac, we make three formulas for Fc Ex: A 100 kg astronaut in training is spinning in a centrifuge. Determine the centripetal force acting on the person if the centrifuge has a 8.80 m radius and spins at 10.0 m/s.
How many “g’s” is this?
Ex: Same astronaut, same centrifuge but up the speed to 15.0 m/s.
How many “g’s” is this? Ex: A 5.0 kg mass rotates in a circle with a 6.0 m radius. If the centripetal force applied is 47.4 N, what is the time for one revolution?
Ex 11: Determine the centripetal force acting on a 100 kg man in a 8.80m radius centrifuge if he is spinning at 15 rpm. 5.3 Horizontal and Vertical Circular Motion
Horizontal Circular Motion
o most common example – cars going around corners
o very important to civil engineers
Ex 1: Determine the maximum speed at which a 1500 kg car can round a curve that has a radius of 40.0 m if the static coefficient of friction is 0.60.
Ex 2: An Edmonton Oiler (m = 100 kg) carves a turn with a radius of 7.17 m while skating and feels his skates begin to slip. What is his speed of the coefficient of static friction between the skates and ice is 0.80?
Ex 3: Automotive manufacturers test the handling ability of a new car by driving a prototype on a test track in a large circle (r=100 m) at increasing speeds until the car begins to skid. A prototype car (m=1200 kg) is tested and found to skid at 95 km/h. Determine the coefficient of static friction between the car and tires.
Ex 4: A 600.0 g toy radio controlled car can make a turn at a speed of 3.0 m/s on the kitchen floor where the coefficient of friction is 0.900. What is the radius of the turn? Vertical Circular Motion
• create unique problems because weight (Fg) becomes a factor
• Fg (weight) never changes but Fc may vary from point to point
The weight of the object ( Fg ) and the tension in the string ( FA ) act in the same direction.
The centripetal force is always the net force that is acting toward the center.
The weight of the object ( Fg ) and the tension in the string ( FA ) act in the same direction.
The centripetal force is always the net force that is acting toward the center.
Ex 5: A 1.8 kg object is swung from the end of a 0.50 m string in a vertical circle. If the time of revolution is 1.2 s, what is the tension in the string at the top of the circle? The weight of the object ( Fg ) and the tension in the string ( FA ) act in opposite directions.
Again, the centripetal force is the net force that is acting toward the center
* not on formula sheet!
Ex 6: Same scenario as example 5, what is the tension in the string at the bottom of the circle?
Minimum Speed
• minimum speed occurs when the tension on the object (FT or Fa) is 0, therefore Fc = Fg
Ex 7: A 700.0 kg roller coaster full of people goes in a vertical loop that has a diameter of 50.0 m. What is the minimum speed the roller coaster must maintain at the top of the vertical loop to stay on the track? Ex 8: A bucket of water with a mass of 1.5 kg is spun in a vertical circle on a rope. The radius of the circle is 0.75 m and the speed of the bucket is 3.00 m/s. What is the tension on the rope in position C, as shown?
Ex 9: A 1.03 x 103 kg car goes over a hill as shown. If the radius of the curve is 40.0 m, how fast must the car travel so that it exerts no force on the road at the crest?