15-cars_curve

15-cars_curve - I. UNIFORM CIRCULAR MOTION Uniform circular...

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v I. UNIFORM CIRCULAR MOTION Uniform circular motion means an object that is going around in a circle at a constant speed. The velocity is continually changing as the direction of motion is always changing. 1. Centripetal Acceleration Note that: (i) the instantaneous velocity , v , is always tangential. This is the direction that a stone in a sling will actually go when the sling is released. (ii) the acceleration is always towards the centre Acceleration going towards the centre is called centripetal acceleration, a c . There is no such thing as centrifugal acceleration – acceleration that pushes something to the outside of a circle. : Think about it a bit. When you are in a car that is turning to the left, you are not being pushed to the outside (the right). You want to keep on going straight (Newton’s First Law). The reason that you don’t go straight is that the car is moving to the left, the side of the car also pushes you to the left ! – that is to the inside of the circle! v and a are perpendicular. If this wasn’t so, you wouldn’t go in a circle. If v suddenly became zero, then the object would just go in the direction of a (the red arrow). If v got smaller slowly, you would spiral into the centre. 2. Formula Any acceleration towards the centre is related to the velocity and radius: r v a c / 2 = Obviously this is a scalar equation – it doesn’t give direction as both v and a are constantly changing (so is r for that matter). We also cannot divide vectors (we may be able to square them). Now for a circle, the distance around it is 2 π r and the time for one revolution is T. v = 2 π r/T or 2 π rf. This means that our formula for acceleration can be written as 2 2 2 2 4 or / 4 rf a T r a c c π = π = 3. Centripetal Force Any force that pushes something towards the centre of a circle is called centripetal force , F c . This is the force that keeps something in circular motion. Centripetal Force is a “pseudo-force” in that there is always some other real force that is pulling the object in. Think of it as a way of describing or classifying other forces. Possible centripetal forces include gravity, tension, friction, the normal force, electromagnetic force. All centripetal forces are also equal to F c = ma c which gives r mv F c / 2 = <Nelson: p 126 #4 – 10> NEED EXAMPLES TO WRITE ON BOARD. ALSO QUESTIONS FROM GIANCOLI NOT MUCH ABOUT GRAVITY – IT WILL ALL BE DONE IN THE FIELDS UNIT v r This means that the outer parts of a hard drive are accessed faster. The outer partitions are fastest!

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II. CARS GOING AROUND CURVES For problems involving cars going around a curve, we use centripetal force and another (real) force. F
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This note was uploaded on 11/23/2010 for the course CIVIL 105 taught by Professor No during the Spring '10 term at Lovely Professional University.

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15-cars_curve - I. UNIFORM CIRCULAR MOTION Uniform circular...

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