Consider two identical rods with lengthLand uniformly distributed massM. The rods are not pinned down, they are free to move both translationally and rotationally. Initially, the center of mass of each rod is stationary, but the left rod is rotating clockwise around its center with an angular speedω0(the right rod is not rotating): The ends of the rods collide. After the collision, the left rod moves directly up towards the top of the page with a speedv, and is no longer rotating around its center: If the collision is elastic, find expressions for the following quantities: - the speedv
- the final translational velocity of the center of mass of the right rod - the final angular velocity of the right rod around its center Express your answers in terms ofω0,L, and numerical factors.

Question

09-12-2022
Physics

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Consider two identical rods with lengthLand uniformly distributed massM. The rods are not pinned down, they are free to move both translationally and rotationally. Initially, the center of mass of each rod is stationary, but the left rod is rotating clockwise around its center with an angular speedω0(the right rod is not rotating): The ends of the rods collide. After the collision, the left rod moves directly up towards the top of the page with a speedv, and is no longer rotating around its center: If the collision is elastic, find expressions for the following quantities: - the speedv
- the final translational velocity of the center of mass of the right rod - the final angular velocity of the right rod around its center Express your answers in terms ofω0,L, and numerical factors.

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jaspreetsharma jaspreetsharma · Answer 1 · 2022-12-19T03:18:06+01:00

The centre of mass of the right rod has a final translational velocity of MWo2/12. The right rod's final angle of rotation about its centre is ML2/12.

Ordinary velocity, expressed in metres per second, is what translational velocity is. Tangential velocity is the part of ordinary (translational) velocity that is in the tangential direction. For instance, if a rigid body is rotating about a fixed axis at an angular velocity of radians per second, any point r metres away from the axis will have a purely tangential velocity of r metres per second. The speed at which the angular location or orientation of an item varies is represented by a pseudovector in physics as angular velocity or rotational velocity ( or ), also called an angular frequency vector.

Iz = Ix+Iy

Ix = iy

Iz = 2Ix

(ML^2/6)/2 = ML^2/12

the final angular velocity of the right rod around its center is ML^2/12.

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