# Worksheet: Coordinate Systems

In this worksheet, we will practice performing vector calculations in different coordinate systems such as polar, cylindrical, and spherical coordinates.

Q1:

Consider a coordinate system in which the positive -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?

• A
• B
• C
• D
• E

Q3:

Two points in the Cartesian plane have the coordinates and . Find the distance between them.

Q4:

Two points in a plane have polar coordinates and .

Determine the Cartesian coordinates of .

• A(2.115 m, 1.210 m)
• B(2.165 m, 1.250 m)
• C(2.225 m, 1.150 m)
• D(2.265 m, 1.130 m)
• E(2.100 m, 1.050 m)

Determine the Cartesian coordinates of .

• A( m, 3.095 m)
• B( m, 3.290 m)
• C( m, 3.140 m)
• D( m, 3.050 m)
• E( m, 3.000 m)

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 that is directly over the North Pole to a point that is at a latitude of . In determining the motion of the satellite, use a value of 6,371 km for the radius of Earth.

What is the magnitude of the displacement vector from to ?

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

Q6:

Under which conditions should coriolis acceleration be considered?

• Awhen translating reference frames are used
• Bwhen co-moving reference frames are used
• Cwhen rotating reference frames are used
• Dwhen linearly accelerating reference frames are used
• Ewhen fixed reference frames are used

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?

• AThe floor should be a coordinate of zero, and the upward direction should be considered positive.
• BHer hand should be a coordinate of zero, and the upward direction should be considered positive.
• CThe floor should be a coordinate of zero, and the downward direction should be considered negative.
• DHer hand should be a coordinate of zero, and the downward direction should be considered positive.