Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
1.7k views
in Physics by (8.8k points)

 Motion in two dimensions, in a plane can be studied by expressing position, velocity and acceleration as vectors in Cartesian co-ordinates A = Ax cap i + Ay cap j  where  cap i and cap j are unit vector along x and y directions, respectively and Ax and Ay are corresponding components of A (Fig. 4.9). Motion can also be studied by expressing vectors in circular polar co-ordinates as A = Ar cap r + Aθ cap θ where cap r = r/r cosθ sinθ and are unit vectors along direction in which ‘r’ and ‘θ ’ are increasing.

(a) Express cap i and cap j in terms of cap r and cap θ

(b) Show that both cap r and cap θ  are unit vectors and are perpendicular to each other

(c) Show that (d/dt) (cap r) = ω cap θ where

(d) For a particle moving along a spiral given by r = aθ cap r , where a = 1 (unit), find dimensions of ‘a’.

(e) Find velocity and acceleration in polar vector represention for particle moving along spiral described in (d) above.

 

Please log in or register to answer this question.

1 Answer

+1 vote
by (13.8k points)

V = ω cap ωθ cap θ and a =

 

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...