Angular Mechanics - Centripetal and radial accel

Contents:•Review

•Tangential Relationships•Radial vs tangential•Centripetal acceleration | Whiteboard

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

Angular Mechanics – Tangential and radial

TOC

Radial

Tangential: a = r

r

= -Centripetal

Angular Mechanics – Centripetal Acceleration

TOC

a = v2/rv = ra = v2/r = (r)2/r = 2r2/r = 2r

a = 2r

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

Whiteboards: Centripetal acceleration

1 | 2 | 3

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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

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

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