MATH 241 Lecture Notes - Lecture 9: Unit Vector

• School: University of Maryland
• Department: Mathematics
• Course: MATH 241
• Professor: Christian Rosendal

Document Summary

Math241 lecture 9 tangents and normal. It will be useful to find two unit vectors at any point, one will be tangent to the curve and the other normal (perpendicular). Definition: given a parameterization (cid:1870) (cid:4666)(cid:1872)(cid:4667) the tangent vector to the curve is the vector. Well, (cid:1870) (cid:4666)(cid:1872)(cid:4667) (acceleration which captures changes in speed and change in direction) captures. Direction is captured by (cid:1870) (cid:4666)(cid:1872)(cid:4667) (unit vector so length will be 1), so: two concepts, change of speed and change of direction. Definition: the normal vector to the curve is. So is perpendicular to , since is a multiple of . We know that is perpendicular to as well. Do not need to know this proof! (cid:1870) (cid:4666)(cid:1872)(cid:4667)=(cid:1872)(cid:2870)(cid:2835) +(cid:1872)(cid:2836) . That acceleration can be broken into two components, one tangent to direction of motion and one perpendicular (normal) to direction of motion. Find the tangent and normal components of acceleration at (cid:1872)=(cid:889).