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Torque, Equilibrium, & Dynamics
Torque Dynamics Rotational Inertia Angular Acceleration Equilibrium Rotational Energy Angular Momentum
Torque,
r
F
rFsin()= r F = r F
Torque,
r
F
r F
F
Torque,
r
F
r F
r
Torque
x
yFx
Fy
€
r = rr ×
r F = rF sinθ
r τ = (Fx y − Fyx) ˆ k
i x i = j x j = k x k = 0
i x j = kj x k = i x y z x y zk x i = j
j x i = -kk 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
+ + + +
---
Angular momentum
L = mvrsin= mv r
L = mrv = mr2= I
=I=I /t = L/t
=L/t
r
v
€
rL =
r r ×
r p = rp sinθ
Conservation of Angular Momentum
If = 0 then L is constant.
Usually, L=m v r Or L = I
r1=4.0 m & v1=3.0 m/s v2=? When r2=1.5 m
=L/t
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