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Lecture_7

# Lecture_7 - acceleration Examples – Spinning a rock on a...

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Circular Motion & Gravitation

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Ball in a Ring
Uniform Circular Motion Circular motion with a constant speed Since direction is always changing, so is velocity Velocity vector is tangent to the circle

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Basic Properties Properties can be derived by basic definitions The period, T (time it takes to complete one rotation), is: For objects taking the same time to complete a circuit, the velocity of the object at greatest radius is the greatest. T = 2 π r v
Centripetal Acceleration Velocity is always changing direction so the object is accelerating. a c = v 2 r

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Forces on Objects with Circular Motion An object moving in a circle must have acceleration of a c . There must be a force(s) to provide this

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Unformatted text preview: acceleration. Examples: – Spinning a rock on a string – Car on a curve – Roller coaster loop – Orbits of celestial bodies ∑ ⃗ F = m ⃗ a c Example: Swinging Weight Lifter Example: Car on a Curve Example: Vertical Circle ∑ ⃗ F = mv 2 r = mg − N ∑ ⃗ F = mv 2 r = N − mg ∑ ⃗ F = mv 2 r = T bottom − mg ∑ ⃗ F = mv 2 r = T top + mg Non-uniform circular motion Newton's Law of Gravitation Acts on both masses involved Distance between the centers of the objects Always attractive Acts along the line connecting the centers of the objects. F grav = Gm 1 m 2 r 2 g = G M Earth r Earth 2 Cavendish Experiment...
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Lecture_7 - acceleration Examples – Spinning a rock on a...

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