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Angular Mechanics - Centripetal and radial accel
Contents:•Review
•Tangential Relationships•Radial vs tangential•Centripetal acceleration | Whiteboard
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Angular Mechanics - Tangential Relationships
Linear:(m) s
(m/s) v(m/s/s) a
Tangential: (at the edge of the wheel)
= r - Displacement
= r - Velocity
= r - Acceleration* - tangential
TOC*Not in data packet
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Angular Mechanics – Tangential and radial
TOC
Radial
Tangential: a = r
r
= -Centripetal
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Angular Mechanics – Centripetal Acceleration
TOC
a = v2/rv = ra = v2/r = (r)2/r = 2r2/r = 2r
a = 2r
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Example: What’s the centripetal acceleration 5.0 cm from the axis of a 10,000 RPM centrifuge?
= 2(10,000rev/min)/(60 sec/min) = 1047.19 s-1
r = .050 ma = 2r = (1047.19 s-1)2 (.050 m) = 55,000 m/s2
TOC
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Whiteboards: Centripetal acceleration
1 | 2 | 3
TOC
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What is the centripetal acceleration of a point 35 cm from an axis of a wheel that has an angular velocity of 12 rad/s?
a = 2r , r = .35 ma = (12 rad/s)2(.35 m) = 50. m/s/s
50. m/s/s W
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A car has 68 cm diameter wheels, and is going at a constant speed of 32 m/s. What is the tangential acceleration, and what is the radial acceleration? (centrip)
a = 2r , r = .68/2 m, v = r, = v/rr = .34 m = (32 m/s)/(.34 m) = 94.118 rad/sa = (94.118 rad/s)2(.34 m) = 3011 m/s/s
3.0E3 m/s/s W
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What is the angular velocity of a centrifuge if it pulls 2000. “g”s with a radius of 6.7 cm? How many RPMs is this?
a = 2000(9.8) = 19600 m/s/s, r = .067 ma = 2r, = 540 rad/sRPM = (540rad/s)(60 s/min)(rev/2 rad)RPM = 5164 RPM = 5200 RPM
540 rad/s5200 RPM W