what is motion in plane
Answers
Motion in a plane includes linear motion, rotational motion, and projectile motion.
Motion can occur in one-dimension, in two-dimensions or in three-dimensions. Planar motion is when an object moves in two directions at the same time. For example, walking North and East simultaneously (Northeast) at a rapid rate of speed to get away from someone begging you to do their physics homework for them is planar motion. The use of a coordinate system is critical when analyzing motion in a plane. We use unit-vectors to designate direction along the axes. All unit-vectors have a magnitude of one and point in the positive direction of their axis. The symbol for a unit vector is a letter with a caret symbol over it. The x-direction unit vector is î, also known as i-hat. We use j-hat for the y-direction and k-hat for the positive z-direction.
3-D coordinate system showing unit-vectors.
ijkvectors
Linear Motion of a Single Object in Two-dimensions
Let's say we have a mass that started at the origin and three seconds into its motion reached point Q located at 4 meters along the negative x-axis and 3 meters up the positive z-axis. We would represent this mass's position at t = 3 s in three-dimensions (x,y,z) as (-4,0,3). Figure 1 shows point Q with its displacement vector (red arrow) from the origin to point Q in a three-dimensional grid. A three-dimensional grid is used to illustrate the two-dimensional plane that the mass is in. Our mass is in the x-z plane.
Figure 1. The displacement vector is written in unit vector notation.
2dposition
The mass at point Q was initially traveling at velocity
velocity_vector
and suddenly at position coordinates (-4 m, 0 m, 3 m) it experienced a force giving it an x-direction acceleration.
acceleration_vector
We could only measure the x-direction acceleration, and the mass eventually ended up back at the origin. What was the mass's acceleration in the z-direction?
Since we are dealing with motion in a plane we must treat the motion in each direction separately. It is best to start with a kinematic equation containing the variables that you have been given and the variable you are asked to determine.