Question

A wildland fire sawyer is cutting a snag of length L = 17.5m and mass m = 820kg. He puts a Humboldt face cut on the snag which has a negligible amount of taper, and we can assume the dead tree is a thin rod. If the snag is initially at an angle of 90o from the horizontal before it begins to sway and fall, the what is the final angular velocity of the snag when it hits a horizontal surface?

Answer 1

given

L = 17.5 m

m = 820 kg

using law of conservation of energy

0.5 I ² = m g L/2

here I = m L² / 12 + m (L/2)²

I = mL² / 3

0.5 (mL²/3) ² = m g L/2

0.5 (L/3) ² = g/2

² = 3g/L

² = 3 X 9.8 /17.5

² = 1.68

= 1.2961 rad/sec

so the final angular velocity of the snag when it hits

a horizontal surface is = 1.2961 rad/sec