Physics circular motion

# Physics circular motion - Physics 101 Lecture 7 Uniform...

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1 PHYS 101 -- Lecture 7 1 In this lecture (Giancoli Chapter 5): - Uniform circular motion Constant speed, circular path Acceleration v 2 /r toward centre - Centripetal vs. centrifugal - Cornering in vehicles and the role of friction - Banked curves Physics 101 – Lecture 7 Uniform Circular Motion and Gravitation PHYS 101 -- Lecture 7 2 One of the simplest types of non-linear motion is uniform circular motion . v Firstly, the kinematics of uniform circular motion: . Consider a whirling object on the end of a rope: constant speed circular trajectory

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2 PHYS 101 -- Lecture 7 3 v 1 Clearly the direction of motion is changing; this means the velocity is changing , and this implies there is acceleration . So from Newton’s second law, there must be a force acting . changing velocity barb4right acceleration barb4right force v 2 PHYS 101 -- Lecture 7 4 Let’s calculate the acceleration. It is: a = ∆v/∆t = (v 2 – v 1 )/(t 2 – t 1 ) If we do this at two points 1 & 2 (for example, at 90 o apart on the circle), we get the diagrams at right. v 1 Note that the vector ∆v is oriented towards the center of the circle Of course, the instantaneous acceleration a is the result of the above equation when ∆t shrinks to zero. v 2 v 2 -v 1 ∆v
3 PHYS 101 -- Lecture 7 5 As we shrink ∆t, we get a situation like this diagram, and the general result stays valid: In uniform circular motion, acceleration is always directed towards the centre of the circle ! This is sometimes called centripetal acceleration (NOT centrifugal!) or radial acceleration . What is the magnitude of this acceleration? Consider the triangle ABC where C is the centre of the circle.

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