1. Circular Motion Uniform Circular Motion Acceleration
Forces in Circular Motion
Banked curves
Centripetal forces
Centrifugal vs. Centripetal Force

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3. Uniform Circular Motion
The speed and radius of an object remains constant
The velocity vector changes because its direction changes.

4. Acceleration
A moving body undergoes acceleration if its speed or direction changes.
Uniform Circular Motion produces Centripetal Acceleration.
“Centripetal” from Latin:
Centrum = “centre”; Petere = “to seek”

5. Centripetal Acceleration
Centripetal acceleration is an instantaneous acceleration
It always acts towards to the center of motion.

6. Centripetal Acceleration
……………….
It points toward the center of the circular path of motion.

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8. Check Your Understanding
A child on a merry-go-round is 4.4 m from the centre of the ride, travelling at a constant speed of 1.8 m/s. Determine the magnitude of the child’s centripetal acceleration.
Answer: ac = 1.82/4.4 = 0.74 m/s2

9. The ac formula can be written as:
……………
For high rates of revolution, it is common to state the frequency rather than period. The frequency f = the number of revolutions per second = 1/T.

10. Our Equations for Uniform Circular Motion
If speed (v) is known:
If speed is not known but period (T) is:
If f is used in place of T due to a high revolution rate

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12. Check Your Understanding
Determine the frequency and period of rotation of an electric fan if a spot at the end of one fan blade is 15 cm from the centre and has a centripetal acceleration of magnitude 2.37 x 103 m/s2. Answer: T = s/rev f = 2.0 x 10 rev/s

13. Forces in Circular Motion

14. Analyzing Forces in Uniform Circular Motion
According to Newton’s Second Law, there is a net force acting towards the centre of the circle that causes the centripetal acceleration.

15. The equations for centripetal acceleration involving the period and frequency of circular motion can also be combined with the second-law equation. Thus, there are three common ways of writing the equation:
Fnet is the magnitude of the net force that causes the circular motion

16. Check Your Understanding
A car of mass 1.1 x 103 kg negotiates a level curve at a constant speed of 22 m/s. The curve has a radius of 85 m.
Name the force that provides the centripetal acceleration.
Determine ……………..
Determine the minimum coefficient of static friction needed to keep the car on the road.

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20. Check Your Understanding
A 3.5-kg steel ball in a structural engineering lab swings on the end of a rigid steel rod at a constant speed in a vertical circle of radius 1.2 m, at a frequency of 1.0 Hz, as shown below. Calculate the magnitude of the tension in the rod due to the mass at the top (A) and the bottom (B) positions. Answers: Position (A) – FT = 1.3 x 102 N Position (B) – FT = 2.0 x 102 N

21. Centripetal forces
What forces can cause something to move in a circle?
Tension, Gravity (components if on earth or full force if considering orbits)
Force of Static Friction
These forces constantly counteract the bodies desire to move away from the circular path on a tangent.
Note: all forces that are centre seeking are centripetal forces

22. Centrifugal vs. Centripetal Force
Centrifugal force (Latin for "center fleeing") describes the tendency of an object following a curved path to fly outwards, away from the center of the curve.
It's not really a force; it results from inertia i.e. the tendency of an object to resist any change in its state of rest or motion. 
Centripetal force is a "real" force that counteracts the centrifugal force and ……………..

23. Human Centrifuge Rick Mercer in a human centrifuge
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