Brakes, Springs, & Flywheels

$\frac{F_1}{F_2}=e^{f\theta}

$T=F_{net}r=F_{net}\frac{D}{2}$

$P=\frac{NT}{factor}

$F_{net}=F_1-F_2

$M_h=F_2a-F_aL=0

$P_{max}=\frac{F_1}{br}

$S_{max}=\frac{F_1}{bt}

$M_h=F_2(c)-F_1(b)-F_a(a)=0

$C=\frac{D_m}{d_w}$
$C=\frac{D_o-d_w}{d_w}$
$C=\frac{D_i+d_w}{d_w}$

$D_m={D_o-d_w}$
$D_m=D_i+d_w$
$D_m=\frac{D_i+D_o}{2}

$K_w=\frac{4c-1}{4c-4}+\frac{0.615}{c}

$S_s=\frac{8K_wFc}{πd_w^2}

$K_s=1+\frac{1}{2c}

$K_c=\frac{K_w}{K_s}

$K_B=\frac{4c+2}{4c-3}$
$K_B=0.99K_w

$\delta=\frac{8Fc^3n}{Gd_w}

$n$
$L_{solid}=(n+1)d_w$
$L_{free}=np+d_w

$n$
$L_{solid}=nd_w$
$L_{free}=np

$n+2$
$L_{solid}=(n+3)d_w$
$L_{free}=np+3d_w

$n+2$
$L_{solid}=(n+2)d_w$
$L_{free}=np+2d_w

$k=\frac{F}{\delta}

$\frac{1}{k_T}=\frac{1}{k_1}+\frac{1}{k_2}$
$k_T=\left(\sum\frac{1}{k}\right)^{-1}$

$F_T=F_1=F_2$
$\delta_T=\delta_1+\delta_2

${k_T}={k_1}+{k_2}$
$k_T=\sum{k}$

$F_T=F_1+F_2$
$\delta_T=\delta_1=\delta_2

$SE=\frac{1}{2}F\delta$
$SE=\frac{1}{2}k\delta^2$

$PE=w(h+\delta)

$KE=\frac{1}{2}mv^2

$S=\frac{6FL}{bt^2n}

$\delta=\frac{SL^2}{Et}

$S=\frac{6FL}{bt^2}\left(\frac{3}{2n_g+3n_f}\right)

$\delta=\frac{SL^2}{Et}\left(\frac{2}{3}\right)

$P=2π\sqrt{\frac{m}{k}}

$F=\frac{1}{2π}\sqrt{\frac{k}{m}}

$W_{fylwheel}=W_{rim}+W{armshub}

$W_{rim}=\gamma V_{rim}$

$\gamma_{steel}=7850 \frac{kg}{m^3}=0.284\frac{lb}{in^3}

$∆KE=\frac{1}{2}m_f(v_1^2-v_2^2)$
$∆KE=\frac{1}{2}\frac{W_f}{g}(v_1^2-v_2^2)$

$KE=\frac{1}{2}I\omega²$
$KE=\frac{1}{2}mr²\omega²

$v=πD_mN$
$v=2πR_mN

$C_f=\frac{v_1-v_2}{v_{mean}}$
$C_f=\frac{N_1-N_2}{N_{mean}}

$∆KE=\frac{W_fC_f}{g}(v_m^2)

$S_{su}=\frac{F}{πDt}$
$F=S_{su}πDt

$Energy=\frac{1}{2}(Force)(Thickness)$
$E=\frac{1}{2}S_{su}πDt^2

$P=\frac{Energy}{Time}

$P=\frac{Perimeter}{3}t(k)

$k_{steel}=80\frac{tons}{in^2}$
$k_{brass}=65\frac{tons}{in^2}

$P=80dt(steel)$
$P=65dt(brass)