The motion of an object moving in a

curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line (geometry), line, but that does not have to be Linearity, straight. Intuitively, a curve may be thought of as the trace left by a moving point (ge ...

d path is called curvilinear motion. Example: A

stone In geology, rock (or stone) is any naturally occurring solid mass or aggregate of minerals or mineraloid matter. It is categorized by the minerals included, its Chemical compound, chemical composition, and the way in which it is formed. Rocks ...

thrown into the air at an

angle In Euclidean geometry, an angle is the figure formed by two Ray (geometry), rays, called the ''Side (plane geometry), sides'' of the angle, sharing a common endpoint, called the ''vertex (geometry), vertex'' of the angle. Angles formed by two ...

. Curvilinear motion describes the motion of a moving particle that conforms to a known or fixed curve. The study of such motion involves the use of two co-ordinate systems, the first being planar motion and the latter being cylindrical motion.

Planar motion

In planar motion, the

velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...

and

acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...

components of the particle are always tangential and normal to the fixed curve. The velocity is always tangential to the curve and the acceleration can be broken up into both a tangential and normal component.

Cylindrical components

With cylindrical co-ordinates which are described as î and j, the motion is best described in polar form with components that resemble

polar vector In physics and mathematics, a pseudovector (or axial vector) is a quantity that is defined as a function of some vectors or other geometric shapes, that resembles a vector, and behaves like a vector in many situations, but is changed into its op ...

s. As with planar motion, the velocity is always tangential to the curve, but in this form acceleration consist of different intermediate components that can now run along the radius and its normal vector. This type of co-ordinate system is best used when the motion is restricted to the plane upon which it travels.

References

{{reflist Motion (physics)