Crash Course: Uniform Circular Motion. Our next test will be the week of Nov 27 Dec 1 and will cover projectiles and circular motion.


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1 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) Crash Course: Uniform Circular Motion Our next test will be the week of Nov 27 Dec 1 and will cover projectiles and circular motion Outcomes 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! Gravitron 1
2 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. Applications 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! Centripetal a 2
3 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 Centripetal a 3
4 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 a c. 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. Centripetal Force 4
5 Centripetal Force Example 1 5
6 Example 1 Example 2 6
7 Example 2 Example 2 7
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10 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 Rotational Motion 10
11 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: Rotational Motion Banked Curves Land 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. Banked Curves 11
12 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. Banked Curves 12
13 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. This formula shows us that as velocity increases, so must the angle of banking. Notice that the mass doesn't matter. Banked Curves Nov 15 7:03 PM 13
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