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L7-Rotation

# L7-Rotation - Rotation Physics 7B Lecture 7 Prof John...

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Rotation Physics 7B - Lecture 7 Prof. John Conway

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Bicycles - PRS If you are on a bicycle standing still, you will fall over very quickly. If the bike is moving you do not fall over as easily, because a. it’s easier to turn against the fall when moving. b. the rotating wheels generate a torque that keeps the bike from falling. c. the force of gravity on rotating objects is reduced. d. it takes more torque to cause the bike to fall over when the wheels are rotating. e. the rotating wheels tend to be vertical due to their angular momentum.
New Terms We’ll Master angular velocity how fast something rotates rotational inertia (a.k.a. moment of inertia) “rotational” mass angular momentum quantity of rotational motion torque angular force Each of these concepts has a direct analog with linear motion

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Angular Linear quantity linear angular position x θ velocity v ω mass m I momentum p = mv L = I ω force F τ energy 1/2 mv 2 1/2 I ω 2 impulse F Δ t τ Δ t
Angular Velocity ω is the Greek letter omega (NOT w !) ω is called the angular velocity units of angular velocity: radians per second, or simply s -1 (same as frequency!!) 1 revolution = 2 π radians rev/sec = ω /2 π

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Circular motion Two masses connected by rod: dumbbell No net displacement! Position, velocity, momentum vectors are moving
Circular Motion Vectors r - a - v - v = ω r a = ω 2 r

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Angular Velocity Angular velocity for constant rotation: θ (t)= ω t ω =d θ /dt Our dumbbell has no linear momentum, but it does have angular momentum
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