Circular Motion Notes
1
November 29, 2017
Outcomes
Curriculum Outcomes
Circular Motion (8 hours)¨ describe uniform circular motion using algebraic and vector analysis (325‑12)¨ explain quantitatively circular motion using Newton’s laws (325‑13)
Our next test will be the week of Nov 27‑ Dec 1 and will cover projectiles and circular motion
Crash Course: Uniform Circular Motion
Gravitron
The Gravitron is an amusement park ride that takes advantage of some cool consequences of circular motion. The ride spins so fast, that you stick to the surface and don't fall out, even when the ride tilts and you're facing the ground!
https://www.youtube.com/watch?v=bpFK2VCRHUs&list=PL8dPuuaLjXtN0ge7yDk_UA0ldZJdhwkoV&index=7
Circular Motion Notes
2
November 29, 2017
Applications
Some other technologies that involve circular motion are motors, power generators, wheels, fans, and vehicles driving around curves.
Some examples from nature are tornados and hurricanes.
Centripetal a
Centripetal Acceleration
When an object is moving in a circle and its speed is constant, it is said to be moving with uniform circular motion.
The direction of the object's velocity is always tangent to the circle, and is therefore always changing ‑ this means it is always accelerating!
Circular Motion Notes
3
November 29, 2017
Centripetal a
Centripetal Acceleration
If you did some crazy hard math, you could prove that the acceleration vector always points in toward the centre of the circle.
This is called centripetal acceleration, and is calculated using the magnitude of the velocity and radius of the circular path.
Centripetal a
Circular Motion Notes
4
November 29, 2017
Centripetal Force
Centripetal Force
We know from Physics 11 that acceleration is caused by forces, so there must be a force that pushes in the direction of ac.
We call this the centripetal force. It is not a new type of force, but a new label that can be given to other existing forces, like gravity, friction, or tension.
Centripetal Force
• Gravity acts as the centripetal force that keeps planets moving along their orbital paths.
• Friction acts as the centripetal force that keeps a car on the road when taking a sharp turn.
• Tension acts as the centripetal force that keeps an object in motion when swinging around in a circle on a string
In all cases, the centripetal force is provided by another existing force, & acts toward the centre of the object's circular path.
Circular Motion Notes
5
November 29, 2017
Centripetal Force
Example 1
Circular Motion Notes
6
November 29, 2017
Example 1
Example 2
Circular Motion Notes
7
November 29, 2017
Example 2
Example 2
Circular Motion Notes
8
November 29, 2017
p. 559 #1519
Nov 209:36 AM
Circular Motion Notes
9
November 29, 2017
Nov 209:40 AM
Nov 209:53 AM
Circular Motion Notes
10
November 29, 2017
Rotational Motion
Describing Rotational Motion
Recall from the Waves unit of Physics 11 that waves with periodic motion can be described using frequency and period.
Quantity Symbol Units
Rotational Motion
Describing Rotational Motion
Recall from the Waves unit of Physics 11 that waves with periodic motion can be described using frequency and period.
Quantity Symbol Units
Circular Motion Notes
11
November 29, 2017
Rotational Motion
Describing Rotational Motion
Again, by doing a bunch of magic rearranging and substituting involving formulas for frequency/period, circumference, velocity, acceleration, and force...
You can get other formulas for centripetal force, this time involving mass, radius, and frequency or period:
Banked Curves
Banked CurvesLand vehicles can use friction between the tires and the road as a centripetal force, but airplanes cannot. Air friction acts opposite the flight of the plane, and can't act perpendicular to the direction of motion even when travelling in uniform circular motion.
Circular Motion Notes
12
November 29, 2017
Banked Curves
In order to travel in uniform circular motion, there still must be a centripetal force. The only way a plane can accomplish this motion is by tilting (banking) the plane so that part of the plane's lift force can act toward the center of the turn.
Banked Curves
In order to travel in uniform circular motion, there still must be a centripetal force. The only way a plane can accomplish this motion is by tilting (banking) the plane so that part of the plane's lift force can act toward the center of the turn.
Circular Motion Notes
13
November 29, 2017
Banked Curves
This formula shows us that as velocity increases, so must the angle of banking. Notice that the mass doesn't matter.
Sometimes roads are banked too ‑ this helps vehicles stay on the road when the frictional force isn't strong enough to keep them on the road. This has the same effect as it does on airplanes, only now the x‑component of the Normal force acts as the centripetal force. If the road is banked properly, friction is not needed at all.
Nov 157:03 PM
Circular Motion Notes
14
November 29, 2017
Example 3
Nov 2010:01 AM
Circular Motion Notes
15
November 29, 2017
p. 566 #2023
Nov 2010:04 AM
Circular Motion Notes
16
November 29, 2017
Nov 2010:04 AM
Page 1Page 2Page 3Page 4Page 5Page 6Page 7Page 8Page 9Page 10Page 11Page 12Page 13Page 14Page 15Page 16