Transcript angular acceleration

Equations
• Just like kinematics!!!
Circular
q=q0 + wt + ½ at2
w=w0 + at
w2 = w02 +2aDq
a=Dw/Dt
Torque; t = Ia
Linear
d=d0 + vt + ½ at2
v=v0 + at
v2 = v02 +2aDd
a=Dv/Dt
Force; F = ma
Circular motion:
vt = 2pr/T = wr ; tangential velocity
w = 2p/T (rad/sec); angular velocity
T is time to make one rotation or revolution,
one rotation or revolution is 2p radians
Gravity:
F = GmM/r2
Acceleration in circular motion
• Three types
– Angular
• How fast it spins faster
– Tangential
• Linear acceleration at an instant
– Centripetal
• Toward center of rotation
• For now we’ll concentrate on Angular and treat it
just as we did in kinematics;
– Mommy, daddy etc.
Definitions
a = Dw/Dt; angular acceleration, (rad/sec2)
a greek letter “the fish”
at = ar; tangential acceleration, (m/s2)
ac= w2r = vt2/r ; centripetal acceleration
toward center of rotation, (m/s2)
angular acceleration
(Radians per time) per time
a= radians / sec2
a=Dw/Dt
a
at=ar
a
a
ac = vt2 / r = w2r
t
c
q
Circular
q=q0 + wt + ½ at2
w=w0 + at
w2 = w02 +2aDq
a=Dw/Dt
Torque; t = Ia
[arc length, d=rq]
Linear
d=d0 + vt + ½ at2
v=v0 + at
v2 = v02 +2aDd
a=Dv/Dt
Force; F=ma
Circular motion:
vt = 2pr/T = wr ; tangential velocity
w = 2p/T (rad/sec); angular velocity
T is time to make one rotation or revolution,
one rotation or revolution is 2p radians
a = Dw/Dt; angular acceleration
at = ar; tangential acceleration
ac= w2r = vt2/r ; centripetal acceleration toward center
of rotation
Gravity:
F = GmM/r2, PE = -GmM/r, g = GMe/Re2
Worksheet!
• Yeah
1.
2.
3.
A winch winds up 10 meters of steel cable. The
radius of the winch is 0.10 m. How many radians
does the winch turn through to wind up the cable?
If the winch started at rest and finished at 2.0
rad/sec, what was the angular acceleration?
How many seconds did it take?