Exploring Circular Motion and Arc Length Concepts

Who introduced the Cartesian coordinate system?

• Rene Descartes

• Isaac Newton

• Albert Einstein

• Galileo Galilei

What stays constant in polar coordinates during circular motion?

• Theta (θ)

• Radius (r)

• Y-coordinate

• X-coordinate

How is the sine of theta calculated in relation to a circle?

• Hypotenuse over opposite

• Opposite over hypotenuse

• Adjacent over hypotenuse

• Opposite over adjacent

What does angular displacement represent in circular motion?

• Change in angular position

• Change in velocity

• Linear distance traveled

• Change in radius

What is the symbol for arc length?

• l

• s

• θ

• r

What must be the unit for angular displacement when calculating arc length?

• Radians

• Meters

• Degrees

• Centimeters

Why are radians used in the arc length equation?

• Because it's a convention

• Radians are not used in the arc length equation

• To simplify calculations

• To match the units of angular displacement

If the radius is halved while the angular displacement remains the same, what happens to the arc length?

• It is halved

• It remains the same

• It doubles

• It quadruples

What is the equation for circumference?

• πr²

• 2πr

• πd

• rθ

How is the arc length equation related to the equation for circumference?

• Circumference is a special case of the arc length equation

• They are equivalent in all cases

• They are unrelated

• Arc length is derived from circumference