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

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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