Linear motion

Linear motion, also called rectilinear motion,^[1] is one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension. The linear motion can be of two types: uniform linear motion, with constant velocity (zero acceleration); and non-uniform linear motion, with variable velocity (non-zero acceleration). The motion of a particle (a point-like object) along a line can be described by its position $x$ , which varies with $t$ (time). An example of linear motion is an athlete running a 100-meter dash along a straight track.^[2]

For the class of linkages, see straight line mechanism.

Linear motion is the most basic of all motion. According to Newton's first law of motion, objects that do not experience any net force will continue to move in a straight line with a constant velocity until they are subjected to a net force. Under everyday circumstances, external forces such as gravity and friction can cause an object to change the direction of its motion, so that its motion cannot be described as linear.^[3]

One may compare linear motion to general motion. In general motion, a particle's position and velocity are described by vectors, which have a magnitude and direction. In linear motion, the directions of all the vectors describing the system are equal and constant which means the objects move along the same axis and do not change direction. The analysis of such systems may therefore be simplified by neglecting the direction components of the vectors involved and dealing only with the magnitude.^[2]

$t_{1}$ is the time at which the object was at position $\mathbf {x} _{1}$ and

$t_{2}$ is the time at which the object was at position $\mathbf {x} _{2}$

$\mathbf {v} _{\text{i}}$ is the initial velocity

$\mathbf {v} _{\text{f}}$ is the final velocity

$\mathbf {a}$ is acceleration

$\mathbf {d}$ is displacement

$t$ is time

In case of constant acceleration, the four physical quantities acceleration, velocity, time and displacement can be related by using the equations of motion.^[12]^[13]^[14]

Here,

These relationships can be demonstrated graphically. The gradient of a line on a displacement time graph represents the velocity. The gradient of the velocity time graph gives the acceleration while the area under the velocity time graph gives the displacement. The area under a graph of acceleration versus time is equal to the change in velocity.

Angular motion

Centripetal force

Inertial frame of reference

Linear actuator

Linear bearing

Linear motor

Mechanics of planar particle motion

Motion graphs and derivatives

Reciprocating motion

Rectilinear propagation

Uniformly accelerated linear motion

Resnick, Robert and Halliday, David (1966), Physics, Chapter 3 (Vol I and II, Combined edition), Wiley International Edition, Library of Congress Catalog Card No. 66-11527

Tipler P.A., Mosca G., "Physics for Scientists and Engineers", Chapter 2 (5th edition), W. H. Freeman and company: New York and Basing stoke, 2003.

External links[edit]

Media related to Linear movement at Wikimedia Commons