For a particle moving under a central force, it's motion will be
For a particle moving under a central force, it's motion will be Correct Answer in a plane
Concept:
Central force:
- The central force in classical mechanics is defined as the force that is acting on an object which is directed along the line joining the object and the origin.
- The magnitude of the central force depends only on the distance of the object and the centre.
- Due to the central force, the body moves or tends to move in a circular or an elliptical orbit around an axis.
- Since there is no torque due to the central force. So, the angular momentum will remain constant.
- Some example of central forces is gravitational force and electrostatic force.
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Explanation:
Let, r represents the distance of the particle from origin and r̂ is radial direction, than central force
F(r) = F(r)r̂
So the torque acting on it
τ = r × F(r)r̂
⇒ τ = r × F = F(r) (r × r)
⇒ τ = 0 ......(1)
Let p = mv = linear momentum,
Now we know that momentum is also conserved in this case, therefore
Angular momentum L = r × P
r.L = r.(r × p) = 0 ......(2)
Also, to know angle b/w velocity and angular momentum
v.L = v.(r × p) = 0 .....(3)
Hence, from equation (2) and (3), we can see that both the position vector r and the velocity vector v thus lie in the plane perpendicular to L.
Therefore, we can say that, if a particle moving under a central force, its motion will be in phase.
r^r^