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Rotational Motion and the Law of Gravity
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q = (in radians) = angle from 0 r = radius of circle
s = arc length (in radians) q = (in radians)
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If you go all of the way around the circle,
so for s = 360° = 2pr, so q = = 2p rad q (rad) = q (°)
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Angular Displacement Dq =
angular displacement (rad) = change in arc length radius
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If an ant is crawling around the lip of a coffee cup that is 15 cm wide, and walks for 3 cm, what is its angular displacement in radians and degrees? r = 15 cm/2 = 7.5 cm Ds = 3 cm = .4 rad = 22.9°
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Angular Speed Just like linear speed is displacement over time v = Dx/Dt Average angular speed is angular displacement over time wavg = Dq/Dt wavg is “omega average”
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My Mustang has 19” rims. If the tire spins with an angular speed of 45 rad/s, and you time it for 7 s, How many times did it spin? wavg = Dq/Dt wavg = 45rad/s Dt = 7 s Dq = wavgDt = 45 rad/s (7s) = 315 rad One spin = 2p rad rad/2p = 50 spins
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Angular Acceleration Just like linear acceleration is velocity / time
a = Dv/Dt Angular acceleration is angular speed / time = Dw/Dt a = “alpha”
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vt = rw at = ra Tangential Speed = Dt, Dq, w
a b = Dt, Dq, w Which point is moving faster, a or b? vt = rw at = ra
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If time is kept small, tangential speed and acceleration are tangent to the radius
vt at
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Centripetal Acceleration
An object moving in a circle is accelerated toward the center
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Forces that maintain circular motion
Something moving in a circular path has a tendency to want to continue in a tangent path. A force must hold it in its circular path.
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Universal Gravitation
All matter creates a force of gravity with other matter
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Fg = mg
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Find your mass (kg) (weight in lbs ÷ 2.2 lb/kg)
Find “g” on Mars and your weight there, if Mars has a mass of x 1023Kg and average radius of x 106 m. Fg = myou(3.71m/s2) x .455 lb/kg
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