Torque, Equilibrium,

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Torque, Equilibrium, Dynamics

• Torque
• Dynamics
• Rotational Inertia
• Angular Acceleration
• Equilibrium
• Rotational Energy
• Angular Momentum

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Torque, t
q
F
r
trFsin(q) r F r F
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Torque, t
q
F
F
r
tr F
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Torque, t
q
F
r
r
tr F
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Torque
Fy
Fx
y
x
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i x i j x j k x k 0 i x j k j x k i
x y z x y z k x
i j j x i -k k x j -i
i x k -j A x B (Ax i Ay j Az k) x
(Bx i By j Bz k) (Ay Bz - Az By) i (Az
Bx - Ax Bz) j (Ax By - Ay Bx) k




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-
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Angular momentum
v

• L mvrsinq mv r
• L mrv mr2w I w
• t IaI Dw/Dt DL/Dt
• t DL/Dt

r
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Conservation of Angular Momentum

• If St 0 then L is constant.
• Usually,
• Lm v r
• Or L I w

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r14.0 m v13.0 m/s v2? When r21.5 m
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• t DL/Dt

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