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**Rotational Motion Angular Measure (radian) Angular Speed and velocity**

Centripetal Acceleration Centripetal Force Angular Acceleration

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Angular measure y x=r cos(q) r y y=r sin(q) q x x

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**Angular measure s Q= r r s 2p radians = 360° 1.0 radian = 57.3°**

y 1.0 radian = 57.3° s Q= radians r r s q x x

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How far to the moon? Early Greek scientists estimated that the earth’s diameter is 3.5 times larger than the moon’s. If a penny covers up the moon when held 200 cm from your eye, How far is the moon from Earth? (the diameter of a penny is 1.9 cm)

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Small angles h≈ s & r ≈ x r s h q x h/r ≈ s/r ≈ h/x Sin q ≈ q ≈ tan q

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**Angular speed and velocity**

Average angular speed

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**Linear speed and angular speed**

h q x

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**Linear speed and angular speed**

h q x h/r ≈ s/r ≈ h/x Sin q ≈ q ≈ tan q

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Angular acceleration

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Angular acceleration

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**Circular Motion (with constant a)**

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**Circular Motion (constant a)**

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Kinetic Energy

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d

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Torque

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a=? T=?

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**T=? St = Ia TR = 1/2MR2 (a/R) a=? T= 1/2M a mg-T=ma mg- 1/2M a=ma**

mg= (1/2M +m)a mg (1/2M +m) T= 1/2M a SF=ma mg-T=ma a =

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Work and Power

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acac vtvt acac vtvt Where “r” is the radius of the circular path. Centripetal force acts on an object in a circular path, and is directed toward the.

acac vtvt acac vtvt Where “r” is the radius of the circular path. Centripetal force acts on an object in a circular path, and is directed toward the.

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