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Consider:

I need to draw a pulley system as in the figure. How can I do that?

begintikzpicture
 fill[pattern=north east lines] (-3,0) rectangle (3,.3);
 draw(-3,0)--(3,0);
 draw(-2.5,0)--(-2.5,-2.4);
 draw(2.5,0)--(2.5,-1);

 draw[fill=white] (-2.5,-2.4) circle (.3);
 draw[fill=white] (2.5,-1) circle (.3);
 draw[fill=white] (0,-3) circle (.153);

 draw
 (2.5,-1) coordinate (a) node[right] 
 -- (0,-3) coordinate (b) node[left] 
 -- (0,-2.75) coordinate (c) node[above right] 
 pic["$beta$", draw=orange, <->, angle eccentricity=1.2172, angle radius=.51cm]
 angle=a--b--c;

 draw
 (0,-2.75) coordinate (a) node[right] 
 -- (0,-3) coordinate (b) node[left] 
 -- (-2.5,-2.4) coordinate (c) node[above right] 
 pic["$alpha$", draw=orange, <->, angle eccentricity=.72172, angle radius=.751cm]
 angle=a--b--c;
 draw[dashed] (0,-3)--(0,-1);
 draw[fill=white] (-2.5,-2.4) circle (.3);
 draw[fill=white] (2.5,-1) circle (.3);

 draw[fill=white] (0,-3) circle (.153);

endtikzpicture

In order to compute the tangents it is advantageous to make the circles nodes and to use tangent cs:, which comes with calc. And the angles can be conveniently drawn with the angles library, where quotes makes it somewhat simpler to add alpha and beta.

documentclass[tikz,border=3.14mm]standalone
usetikzlibrarypatterns,calc,angles,quotes
begindocument
begintikzpicture
fill[pattern=north east lines] (-3,0) rectangle (3,.3);
 beginscope[thick]
 draw(-3,0)--(3,0);

 path (-2.5,-2.4) node[circle,draw,inner sep=.3cm] (L)
 (2.5,-1) node[circle,draw,inner sep=.3cm] (R)
 (0,-3) node[circle,draw,inner sep=.153cm,label=below:$m$] (M);
 draw (L.north) -- (L.north|-0,0) (R.north) -- (R.north|-0,0);
 draw[dashed] (M) -- (0,-1)coordinate (M1);
 draw (M) -- (tangent cs:node=L,point=(M.center),solution=1) coordinate (L1)
 let p1=($(L1)-(L.center)$),n1=atan2(y1,x1),n2=veclen(y1,x1) in
 arc(n1:180:n2) -- ++(0,-1.5) node[below,draw]$m_1$;
 draw (M) -- (tangent cs:node=R,point=(M.center),solution=2) coordinate (R1)
 let p1=($(R1)-(R.center)$),n1=atan2(y1,x1),n2=veclen(y1,x1) in
 arc(n1:00:n2) -- ++(0,-1.5) node[below,draw]$m_2$;
 endscope
 path pic [draw,angle radius=0.5cm,"$alpha$",angle eccentricity=1.5] angle = M1--M--L1 
 pic [draw,angle radius=0.7cm,"$beta$",angle eccentricity=1.5] angle = R1--M--M1 ;
endtikzpicture
enddocument