what is the angular velocity

Question

a weather vane initially at rest has a moment of inertia of 0.108 kg times m squared about its axis of rotation. a 48.0g piece of clay is thrown at the vane and sticks to it at a point 21.5 cm from the axis. the inital velocity of the clay is 27.0 m/s, directed perpendicular to the vane. find the angular velocity of the weather vane after it is struck.

Answer 1

Use conservation of angular momentum.

 

m = mass of clay = 0.048 kg

r = distance of clay from rotation axis = 0.215 m

I₀ = initial moment of inertia of vane = 0.108 kg m²

I₀ + mr² = final moment of inertia of vane + clay

v = initial speed of clay = 27.0 m/s

 

mvr = (I₀ + mr²)ω ⇒

 

ω = mvr / (I₀ + mr²)

 

You have m, v, r, and I₀.  Just plug in the numbers and get ω in rad/s.