What is the angular speed of the gate?
A uniform square solid wooden gate, weighing 5.50 kg and measuring 2.00 m on each side, hangs vertically from a frictionless pivot located at the center of its upper edge. A raven, weighing 1.30 kg, flies horizontally at a speed of 5.00 m/s and collides with the gate at its center, subsequently bouncing back in the opposite direction at a speed of 2.50 m/s. What is the angular speed of the gate immediately after it is struck by the raven?
3 Answers
Moment of inertia of gate .. I = 1/3. ma² (a = side length)
I = 1/3. 5.50kg x (2m)² .. I = 7.33 kg.m²
Change in ang. mom (mom about the pivot) for raven .. ∆L = mv.r .. (r = 1.0m from pivot)
∆L= 1.30kg x (5.0 + 2.5)m/s x 1.0m .. .. ∆L = 9.75 kg.m²/s .. (taking account of rebound)
Ang. mom. gained by gate (Iω) = change in ang.mom of raven (9.75)
ω = 9.75kg.m²/s / 7.33 kg.m² .. .. .. ►ω = 1.33 rad/s
Nope. The angular speed (velocity) is constant over all radii of the MGR. Call it w. So the gal on the edge is spinning at the same rate as the guy near the middle…w. Then the linear, tangential speed (velocity) is v = wr near the center of the MGR and V = wR near the edge, where R > r. So the person on the edge has a FASTER tangential SPEED, but the SAME angular SPEED. Like linear velocity, angular velocity is made of magnitude (radians per second) and direction (CCW and CW). Spin, rotation, angular speed, motion around the axis, etc. all mean pretty much the same thing.
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