Uniform Circular Motion Pg. 114 - 130

Uniform Circular Motion Occurs when an object moves in a circle and its speed is constant Since direction changes the object experiences centripetal acceleration Note: Centripetal acceleration is always directed toward the centre of the circle

Centripetal Acceleration Practice: 1. A child rides a carousel with a radius of 5.1 m that rotates with a constant speed of 2.2 m/s. Calculate the magnitude of the centripetal acceleration of the child.

Centripetal Acceleration Sometimes you may not know the speed of an object moving with uniform circular motion. However, you may be able to measure the time it takes for the object to move once around the circle, or the period (T) If the object is moving too quickly, you would measure the number of revolutions per unit time, or the frequency (f). Recall: f = 1/T In each case, the equation for centripetal acceleration would become:

(note) Centripetal Acceleration (more)

Practice 2. A salad spinner with a radius of 9.7 cm rotates clockwise with a frequency of 12 Hz. At a given instant, a piece of lettuce is moving in the westward direction. Determine the magnitude and direction of the centripetal acceleration of the lettuce in the spinner at the moment shown (because, doesn’t everybody wonder how fast their lettuce is accelerating when making a salad? )

Practice 3. The centripetal acceleration at the end of a fan blade is 1750 m/s2. The distance between the tip of the fan blade and the centre is 12.0 cm. Calculate the frequency and the period of rotation of the fan.

Centripetal Force According to Newton’s laws of motion, an object will accelerate only if a force is exerted on it. Since an object moving with uniform circular motion is always accelerating, there must always be a force exerted on it in the same direction as the acceleration, as shown:

Centripetal Force Since the force causing a centripetal acceleration is always pointing toward the centre of the circular path, it is called a centripetal force (Fc) Without such a force, objects would not be able to move in a circular path

Centripetal Force Net force that causes centripetal acceleration (Fc = Fnet)

Practice 4. Suppose an astronaut in deep space twirls a yo-yo on a string. A) what type of force causes the yo-yo to travel in a circle? (tension) B) What will happen if the string breaks? (the yo-yp will move along a straight line, obeying Newton’s first law – objects in motion tend to stay in motion) 5. A car with a mass of 2200 kg is rounding a curve on a level road. If the radius of the curvature of the road is 52 m and the coefficient of friction between the tires and the road is 0.70, what is the maximum speed at which the car can make the curve without skidding off the road?

Practice 6. You are playing with a yo-yo with a mass of 225 g. The full length of the string is 1.2m. A) calculate the minimum speed at which you can swing the yo-yo while keeping it on a circular path (hint: at the top of the swing Ft= 0) B) at the speed just determined, what is the tension in the string at the bottom of the swing. 7. A roller coaster car is at the lowest point on its circular track. The radius of curvature is 22 m. The apparent weight of one of the passengers is 3.0 times her true weight (i.e. FN = 3Fg). Determine the speed of the roller coaster

Centripetal Force & Banked Curves Cars and trucks can use friction as a centripetal force. However, the small amount of friction changes with road conditions and can become very small when the roads are icy As well, friction causes wear and tear on tires and causes them to wear out faster For these reasons, the engineers who design highways where speeds are high and large centripetal forces are required incorporate another source of centripetal force – banked curves

Practice 8. What angle of banking would allow a vehicle to move around a curve with a radius of curvature “r” at a speed “v”, without needing any friction to supply part of the centripetal force? (In this case you must resolve FN so that one of the components is directed inward.

Centripetal Force & Banked Curves Take Note: When an airplane is flying straight and horizontally, the wings create a life force (L) that keeps the airplane in the air However, when an airplane need to change directions it must tilt or bank in order to generate a centripetal force The centripetal force created is a component of the lift force, as shown:

Textobook: Pg. 119, #6,8 Pg. 124, #3,4 Pg. 130, #6,7