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. A uniform 4.5 $\mathrm{kg}$ square solid wooden gate 1.5 $\mathrm{m}$ on each side hangs vertically from a frictionless pivot at the center of its upper edge. A 1.1 $\mathrm{kg}$ raven flying horizontally at 5.0 $\mathrm{m} / \mathrm{s}$ flies into this gate at its center and bounces back at 2.0 $\mathrm{m} / \mathrm{s}$ in the opposite direction. (a) What is the angular speed of the gate just after it is struck by the unfortunate raven? (b) During the collision, why is the angular momentum conserved, but not the linear momentum?

a) 1.71 $\mathrm{rad} / \mathrm{s}$b) The linear momentum is conserved when the external force acting on the system is zero. But, inthis scenario the linear momentum is not conserved because the external force acting on the system is not zero.The angular momentum is conserved when the external torque acting on the system is zero.Therefore, in this scenario angular momentum is conserved because external torque acting on the system is zero.

Physics 101 Mechanics

Chapter 10

Dynamics of Rotational Motion

Newton's Laws of Motion

Rotation of Rigid Bodies

Equilibrium and Elasticity

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Well, problem 31 is a conservation of angular momentum problem. We have a uniform square wooden gate that hangs here on this side, and it's frictionless. And we have a rave in that, unfortunately, flies into this center of the gate in bounces back. So we have a collision, and, um, we are looking to find the speed of the gate after the raben hits it. So first, look at this gate to aside calculation here, make sure we know what are moment of inertia of this gate is it is a flat square. Soon we will use 1/3 m. O. R. Squared the gates mass is we're 0.45 kilograms and its length is 1.5. Excuse us. A moment of inertia of 3.375 So this is going to be a conservation of angular momentum problem. Now, before we have looking at our initial and the gate in the initial of the bird unequal. The final of the gate was the final of the bird. Now the gate actually pivots. It's ah. Well, we do know that the gate actually initially is at rest, and its final moment, um, would be I amega final. Now our bird access a particle. We can calculate its angular momentum if we know mass times its initial velocity and how far away from the pivot point it collides or it is. And we'll use the same formula for its final. You know, initially, we're told that it is located. It's coming toward the center here, and it is flying at five meters per second in our maciver bird is 1.1 moving at five meters per second would be located halfway to the pivot point at 0.0.75 Now the gate has a moment of inertia and this is the variable we're actually looking for. What is that? Anguish? Speed of the gate after the collision. And then our good bounces back. So it has a negative velocity of two, and it is still hits and clucked at the same location. Okay, so solving this four final angular speed, we get 1.71 radiance per second. Yeah, four day artsy asks a question about the collision, and they want to know why angular momentum is conserved. Why we can say this right here. But we can't say that linear momentum is conserved. The reason is that there is when the bird comes in and hits the gate and external force added to the closed system. When that happens, we can say.

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