Angular Mechanics Centripetal and radial accel Contents Review

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

Angular Mechanics - Tangential Relationships Linear: Tangential: (at the edge of the wheel) (m) s = r - Displacement* (m/s) v = r - Velocity (m/s/s) a = r - Acceleration* *Not in data packet

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

Angular Mechanics – Centripetal Acceleration a = v 2/r v = r a= 2 r

Example: What’s the centripetal acceleration 5. 0 cm from the axis of a 10, 000 RPM centrifuge? = 2 (10, 000 rev/min)/(60 sec/min) = 1047. 19 s-1 r =. 050 m a = 2 r = (1047. 19 s-1)2 (. 050 m) = 55, 000 m/s 2

Whiteboards: Centripetal acceleration 1|2|3

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

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) = 94. 118 rad/s a = (94. 118 rad/s)2(. 34 m) = 3011 m/s/s 3. 0 E 3 m/s/s

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 = 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