Lecture 3: Motion in two and three dimensions (chap 4 in Halliday) Position Displacement To increasing the dimension is straightforward. Just add more components on the vectors.

Similarly, average velocity and instantaneous velocity are defined as: Or simply: where Same for acceleration:

Projectile motion ( 拋體運動 ): a special case of two dimensional motion. 1.Vertical and horizontal motion are independent. 2.The horizontal motion has no acceleration, i.e. constant velocity. 3.Vertical motion is simply a linear motion (free fall) with constant acceleration discussed in lecture 1.

(a)3,2,1 (b)1,2,3 (c)Same (d)6,5,4

The gravity doesn’t affect the result.

Horizontal motion:Vertical motion: From the above, one has the equation of path (trajectory): x 0 and y 0 = 0 Horizontal range (R):

Horizontal: Vertical:

vertical direction: horizontal direction: eliminate t:

The magnitude v of the velocity does not change, but the direction changes continuously. there is an acceleration: a always pointing towards to the center of the circle. the period is given by: Uniform circular motion ( 圓周運動 ) ( 向心加速度 )

The magnitude of v is: 5s 2s Since v 1 =-v 2, means that it completes half circumference from 2s to 5s, therefore: Average acceleration: