Coordinate Systems Quiz

What is a Coordinate System defined as?

• A mathematical equation

• A reference frame

• A type of graph

• A physical object

Which of the following is NOT a type of coordinate system studied in Physics?

• Hexagonal Coordinate System

• Cylindrical Coordinate System

• Spherical Polar Coordinate System

• Cartesian Coordinate System

In a Cartesian Coordinate System, what do the unit vectors î, ĵ, and k̂ represent?

• The magnitude of a vector

• The direction along the X, Y, and Z axes

• The position of a point

• The velocity of an object

What is the formula for the Position Vector (r) in Cartesian coordinates?

• r = (dx/dt) î + (dy/dt) ĵ + (dz/dt) k̂

• r = x î + y ĵ + z k̂

• r = √(x² + y² + z²)

• r = x + y + z

What does the Velocity Vector (v) represent?

• The rate of change of acceleration with time

• The direction of motion

• The rate of change of position with time

• The distance traveled by an object

In the Spherical Polar Coordinate System, which coordinates are typically used?

• x, y, z

• R, θ, and Φ

• ρ, Φ, and z

• R, θ, and z

What is the relationship between Cartesian coordinates (x, y) and Plane Polar coordinates (R, θ)?

• R = x + y, θ = x - y

• x = R sin θ, y = R cos θ

• R = √(x² + y²), θ = tan⁻¹(y/x)

• x = R cos θ, y = R sin θ

What is the purpose of using Plane Polar coordinates?

• To represent the velocity of an object

• To describe the motion of a cylinder

• To locate a particle on a plane

• To simplify calculations in 3D space

Which of the following is true about the Acceleration Vector (a)?

• It is the rate of change of velocity with time

• It is always constant

• It is the rate of change of position

• It has no relation to time

What does the magnitude of a vector represent?

• The speed of the object

• The length of the vector

• The direction of the vector

• The angle of the vector