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

2. 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
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3. r Angular Mechanics – Tangential and radial Radial = -Centripetal
Tangential: a = r r
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4. 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
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5.  = 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) = s-1
r = .050 m
a = 2r = ( s-1)2 (.050 m) = 55,000 m/s2
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6. Centripetal acceleration
Whiteboards:
Centripetal acceleration
1 | 2 | 3
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7. 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

8. 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) = rad/s
a = ( rad/s)2(.34 m) = 3011 m/s/s W
3.0E3 m/s/s

9. 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 “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 = 2r,  = 540 rad/s
RPM = (540rad/s)(60 s/min)(rev/2 rad)
RPM = 5164 RPM = 5200 RPM
540 rad/s
5200 RPM W