Question

1. Convert the following (x,y) Cartesian coordinates to (r, theta) polar coordinates (record theta first in degrees and then radians):

a) (12,5) [m]

b)(-6.3,2.2) [m]

2. Convert the polar coordinates (13, 5.888) [m, rad] to Cartesian.

3. Find the angular momentum of a 2kg ball relative to the origin if the ball is mivung 3 m/s, 20° north of east the instant it is at (2, -3) [m] in relation to the origin. Sketch all of your vectors and show your work.

4. This example involves a ball colliding with a bar that is able to rotate. Is kinetic energy conserved in the elastic and in-elastic collisions?

Answer 1

. Cartesian coordinates to polar coordinates Given, at (12.5) [m] . In cartesian coordinates x= 12 (ILS) from pig. y = 5 >r = √ 169 - 13 m - (1) also, tan o = 2 900 > 0 = tan' % - tan 5/12 → 0 = 22.6 -(0) In radians 0 = x 22.8 - 53 TT radians, - (3) Inus - from (1) & (ii) the polar coordinates of the Cartesian coordinats (12,5) are (1,0) - (13, 22.6) OR (13,,711) (my radians) A 66 ! 190- from fig. (-6.3, 2.2) [m] flere x=-6.3 (-6.3, 2.2) I 7 = 2.2 s=durge - $ (6.3) 7 (2.252 r = 6.67 Polar coordinates are tan (180-0) = 2.2 (2,0) = (6.67. 160.1) 180-0- tan 2.2/6.3 DR (6.67. 1607) - O- 180 - tan 2.2/6.3 = 160.7" OR 160774 Also, tan (180-0) = 6.3 L800"