Lecture 6

# Lecture 6 - Angular Momentum Lecture 6 John McRaven Angular...

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Angular Momentum Lecture 6 John McRaven

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Angular Momentum Rotating Objects are difficult to describe with regular linear momentum Use angular momentum to describe rotation Angular Momentum has many analogies to linear momentum The Shape of the object must be taken in to consideration for angular momentum
Uniform Circular Motion Uniform Circular Motion occurs when an object moves in a perfect circle at a constant speed Speed is constant, but direction changes, so momentum changes

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Clicker Question What direction is the change in momentum between points 1 and 2? Consider v 1 to be the initial velocity and v 2 to be the final velocity. A) B) C) D)
Uniform Circular Motion The change in momentum is always towards the center of the circle This means the Σ F is always towards the center of the circle Called the centripetal force NOT called the centrifugal force. Σ F Σ F Σ F Σ F Σ F Σ F Σ F Σ F

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Centripetal Force NEVER label a force as the “centripetal force” on a force diagram “centripetal force” is just a name for the actual force causing circular motion. In the case of the earth rotating around the sun, the force is the force of gravity from the sun The force should therefore be labeled as F_Sun_on_Earth , NOT F_Centripetal Σ F Σ F Σ F Σ F
Centripetal Force How big does the centripetal force need to be? It needs to be bigger if the object is moving faster To escape a planets orbit, you must travel faster It needs to be bigger if the object is closer The force of gravity is bigger on planets closer to the sun No Force Not Enough Force Too Much Force Just Enough Force F = m v 2 r

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F = m v 2 r Clicker Question The speed of the earth orbiting around the sun is about 30,000 m/s. The distance from the earth to the sun is about 150 x 10^9 m. The mass of the earth is about 6 x 10^24 kg. How big is the force of gravity on the earth? A) 1.2 x 10^18 N B) 2.6 x 10 ^22 N C) 5 x 10 ^ 20 N D) 4.3 x 10 ^ 21 N
Angular Momentum The direction of the momentum, velocity, and force keep changing throughout the circular momentum Inconvenient to express rotation in terms of linear momentum We can express rotation much more simply with angular momentum . Σ F Σ F Σ F Σ F

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Angular Position Angular Velocity – Rate of Change of the Position Angular Acceleration – Rate of Change of the Velocity θ Angular Kinematic Variables Position – Where an object is Velocity – Rate of Change of the Position Acceleration – Rate of Change of the Velocity v = dx dt a = dv dt x ω = d dt α = d dt
Angular Velocity Frequency:

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Lecture 6 - Angular Momentum Lecture 6 John McRaven Angular...

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