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Transcript Torque

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”
t = torque, “twisting force” units are N.m.
Force at a distance, think turning a wrench
to tighten a bolt.
I = moment of inertia, like mass, only
distribution of mass is important.
Moment of Inertia
• I = sum of mass
times radius from
axis of rotation.
• Fun calculus
problems!
• It has been
cataloged for
common shapes with
uniform density.
I = r 2 dm
I = mr 2
Common I values
(units ?)
point mass I = mr
2
1
solid cylinder, inner radius r, I = m( r 2 R 2 )
2
1
2
thin rod about center, I = mL
12
1 2
thin rod about end, I = mL
3
Worksheet!
• Yeah