What is the angular speed of the gate?

Question

A uniform 5.50 kg square solid wooden gate 2.00m on each side hangs vertically from a frictionless pivot at the center of its upper edge. A 1.30kg raven flying horizontally at 5.00 m/s flies into this door at its center and bounces back at 2.50 m/s in the opposite direction.What is the angular speed of the gate just after it is struck by the unfortunate raven?

Mina Herzog · Accepted Answer

Moment of inertia of gate .. I = 1/3. ma² (a = side length) I = 1/3. 5.50kg x (2m)² .. I = 7.33 kg.m²Change 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

Mina Herzog · Answer

1

Mina Herzog · Answer

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.

Lavinia Carroll

What is the angular speed of the gate?

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