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 *Not in data packet TOC

r Angular Mechanics – Tangential and radial Radial = -Centripetal Tangential: a = r r TOC

a = 2r a = v2/r v = r a = v2/r = (r)2/r = 2r2/r = 2r Angular Mechanics – Centripetal Acceleration a = v2/r v = r a = v2/r = (r)2/r = 2r2/r = 2r a = 2r TOC

 = 2(10,000rev/min)/(60 sec/min) = 1047.19 s-1 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 m a = 2r = (1047.19 s-1)2 (.050 m) = 55,000 m/s2 TOC

Centripetal acceleration Whiteboards: Centripetal acceleration 1 | 2 | 3 TOC

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 m a = (12 rad/s)2(.35 m) = 50. m/s/s W 50. m/s/s

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/r r = .34 m  = (32 m/s)/(.34 m) = 94.118 rad/s a = (94.118 rad/s)2(.34 m) = 3011 m/s/s W 3.0E3 m/s/s

RPM = (540rad/s)(60 s/min)(rev/2 rad) RPM = 5164 RPM = 5200 RPM 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 m a = 2r,  = 540 rad/s RPM = (540rad/s)(60 s/min)(rev/2 rad) RPM = 5164 RPM = 5200 RPM 540 rad/s 5200 RPM W