Posted by **cindy** on Wednesday, March 14, 2012 at 1:55pm.

A weather vane initially at rest has a moment of inertia of 0.115 kg · m2 about its axis of rotation. A 44.5 g piece of clay is thrown at the vane and sticks to it at a point 10.5 cm from the axis. The initial velocity of the clay is 18.5 m/s, directed perpendicular to the vane. Find the angular velocity of the weather vane just after it is struck.

- PHYSICS -
**Elena**, Wednesday, March 14, 2012 at 2:25pm
The moment of inertia of weather vane with piece of clay is

I = I(vane) +mR^2 = 0.115+44.5•10^-3•(0.105)^2=

= 1.2•10^-2 kg • m2.

The torque due to the clay hitting is M=F•R

F•t=Δp=m•v, therefore F=m•v/t.

Then M=F•R=m•v•R/t.

From Newton’s 2 Law for rotation M=I• ε.

m•v•R/t =I•ε.

m•v•R/I= ε• t = ω

ω = m•v•R/I ==44.5•10^-3•18.5•0.105/1.2•10^-2= 7.21 rad•s

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