Find the radial and transverse velocity of a particle moving in a plane
Answers
Explanation:
Radial And Transverse Components
To understand about the radial and transverse components, let us take curvilinear motion.
Shown below is the figure of an object at point P from fixed origin position O and the relationship between radial and transverse components.
The figure shows a particle, point P that moves in a straight motion which results into two components; radial and transverse components. The radial component is denoted as er moving radially in an outward direction from point O to P and the transverse component is denoted as e q.
er and e q are unit vectors and P is the position vector.
The position vector is expressed as
Here, radius from point O to P is r.
Use the product rule and find the general equation for velocity at point P.
The radial velocity refers to the path of an object that moves in a straight line from a fixed point (O).
The transverse velocity refers to an object P that moves in a a path at right angle θ to the origin path from fixed point O.
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Explanation:
In 1 dimensional frame -you can move backward and farward.so, only linear velocity takes place.
In 2 dimension ,3 dimension in course of rotational mechanics,there is both transverse and radial velocity .let’s see…how?…
Radial velocity-is velocity which experiences a body along its radius . It is the time rate of change of {the distance from a fixed reference point}, a.k.a. the radius relative to that fixed reference point. This is quite general, but it is usually used to (partly) describe orbital motion.
Radial velocity is the component of the velocity of a particle along the line of sight of the observer. It is expressed in terms of m/s for equivalent units.
If a distant star is moving away from the line of light of an observer on earth at a linear velocity of, say, 50 m/s, its radial velocity is 50 m/s. Such a star would generally also have a tangential component of its total velocity, which is perpendicular to the radial velocity.
What do we mean by radial velocity?
Consider a particle moving along a curved path.Suppose, at time t it’s radius vector be R and after infinitesimal small interval of time it’ s radius vector becomes R+dR. The velocity by definition will be dR/dt
Therefore, V=dR/dt. Now,resolve displacement vector dR in two components.One in radial direction.This vector component is in the direction of increasing or decreasing R.The other component will be Rd(theta). (theta) is angular displacement Then,
V=(change in the value of R) x unit vector in radial direction.The another component will be Rd(theta)unit vector in the direction of increasing
Transverse velocity-is velocity experienced by a particle along tanget to position of body.so, it also called tangential velocity.
Keep in mind:- radial and transverse/ tangential velocity always be in 90 degree or at right angle.
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