Phy 201: General Physics I Chapter 3: Motion in 2 Dimensions Lecture Notes

2-Dimensional Motion A motion that is not along a straight line is a two- dimensional motion. The position, displacement, velocity and acceleration vectors are necessarily not on the same directions; the rules for vector addition and subtraction apply The instantaneous velocity vector (v) is always tangent to the trajectory but the average velocity (v avg ) is always in the direction of  R The instantaneous acceleration vector (a) is always tangent to the slope of the velocity at each instant in time but the average acceleration (a avg ) is always in the direction of  v R B (t 1 ) R A (t 0 ) v(t)

Example of 2-D Motion

Displacement, Velocity & Accelerations When considering motion problems in 2-D, the definitions for the motion vectors described in Chapter 2 still apply. However, it is useful to break problems into two 1-D problems, usually –Horizontal (x) –Vertical (y) Displacement: Velocity: Acceleration: Use basic trigonometry relations to obtain vertical & horizontal components for all vectors

When t o = 0 and a is constant: Remember: when t o ≠0, replace t with  t in the above equations Equations of Kinematics in 2-D Horizontal: 1.v x - v ox = a x t 2.x - x o = ½ (v ox + v x )t 3.x - x o = v ox t + ½ a x t 2 4.v x 2 - v ox 2 = 2a x  x Vertical: 1.v y - v oy = a y t 2.y - y o = ½ (v oy + v y )t 3.y - y o = v oy t + ½ a y t 2 4.v y 2 - v oy 2 = 2a y  y Projectile Motion is the classic 2-D motion problem –Vertical motion is treated the same as free-fall a y = - g = m/s 2 {downward} –Horizontal motion is independent of vertical motion but connected by time but no acceleration vector in horizontal direction a x = 0 m/s 2 –As with Free Fall Motion, air resistance is neglected

Projectile Motion Notes t x t y t vxvx t vyvy t x t y t vxvx t vyvy

Projectile Motion Notes (cont.)