Angular Mechanics - Centripetal and radial accel Contents: Review Tangential Relationships Radial vs tangential Centripetal acceleration | WhiteboardWhiteboard

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 = v 2 /r v =  r a = v 2 /r = (  r) 2 /r =  2 r 2 /r =  2 r a =  2 r

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) = s -1 r =.050 m a =  2 r = ( s -1 ) 2 (.050 m) = 55,000 m/s 2 TOC

Whiteboards: Centripetal acceleration 11 | 2 | 323 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 =  2 r, r =.35 m a = (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 =  2 r, r =.68/2 m, v =  r,  = v/r r =.34 m  = (32 m/s)/(.34 m) = rad/s a = ( 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 “g”s with a radius of 6.7 cm? How many RPMs is this? a = 2000(9.8) = m/s/s, r =.067 m a =  2 r,  = 540 rad/s RPM = ( 540 rad/s)(60 s/min)(rev/2  rad) RPM = 5164 RPM = 5200 RPM 540 rad/s 5200 RPM W