Lesson: Coordinate Systems

In this lesson, we will learn how to perform vector calculations in different coordinate systems such as polar, cylindrical, and spherical coordinates.

Video

14:07

Sample Question Videos

  • 02:44
  • 01:41

Worksheet: Coordinate Systems • 7 Questions • 2 Videos

Q1:

Consider a coordinate system in which the positive 𝑥 -axis is directed vertically upward.

What is the displacement of a particle 8.5 m directly above the origin?

What is the displacement of a particle 1.3 m directly below the origin?

Q2:

The coordinates of a particle in a rectangular coordinate system are . What is the position vector of the particle?

Q3:

Two points in the Cartesian plane have the coordinates ( 2 . 0 0 , 4 . 0 0 ) m m and ( 3 . 0 0 , 3 . 0 0 ) m m . Find the distance between them.

Q4:

Two points in a plane have polar coordinates 𝑃 2 . 5 0 0 , 𝜋 6 1 m and 𝑃 3 . 8 0 0 , 2 𝜋 3 2 m .

Determine the Cartesian coordinates of 𝑃 1 .

Determine the Cartesian coordinates of 𝑃 2 .

Determine the distance between the points, to the nearest centimeter.

Q5:

A circular polar orbit around Earth is an orbit that passes directly overhead at both the North Pole and the South Pole. A satellite in a circular polar orbit around Earth at an altitude of 400 km moves in its orbit form a point 𝑃 1 that is directly over the North Pole to a point 𝑃 2 that is at a latitude of 4 5 . 0 . In determining the motion of the satellite, use a value of 6 3 7 1 km for the radius of Earth.

What is the magnitude of the displacement vector from 𝑃 1 to 𝑃 2 ?

At what angle below east is the direction of the displacement vector from 𝑃 1 to 𝑃 2 ?

Q6:

Under which conditions should coriolis acceleration be considered?

Q7:

A student is trying to determine the acceleration of a feather as she drops it to the ground. If the student is looking to achieve a positive velocity and positive acceleration, what is the most sensible way to set up her coordinate system?

Preview

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.