For a body, the tangential velocity is on the y-z plane. In what direction will the angular
momentum be?
Answers
Explanation:
The answer is in a new conserved quantity, since all of these scenarios are in closed systems. This new quantity, angular momentum, is analogous to linear momentum. In this chapter, we first define and then explore angular momentum from a variety of viewpoints. First, however, we investigate the angular momentum of a single particle. This allows us to develop angular momentum for a system of particles and for a rigid body that is cylindrically symmetric.The intent of choosing the direction of the angular momentum to be perpendicular to the plane containing →rr→ and →pp→ is similar to choosing the direction of torque to be perpendicular to the plane of →rand→F,r→andF→, as discussed in Fixed-Axis Rotation. The magnitude of the angular momentum is found from the definition of the cross-product,
l=rpsinθ,l=rpsinθ,
where θθ is the angle between →rr→ and →p.p→. The units of angular momentum are kg⋅m2/skg·m2/s.
we have to find out direction of the angular momentum of a body, if the tangential velocity is on the y - z plane.
solution : we know, tangential velocity and position of particle are on the same plane.
so, position, r is also on the y - z plane.
angular momentum, L = m(r × v)
where r is position vector , v is tangential velocity vector.
angular momentum is cross product of position vector and tangential velocity vector. so the direction of angular momentum must be perpendicular to position vector or velocity vector.
we know, x axis perpendicular on y - z plane.
so, direction of the angular momentum will be along x - axis.
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