Polar coordinate system - Quiz
A) r dr dφ B) dr dφ C) dx dy D) dx dr
A) 1 B) sin(φ) C) r2 D) r
A) dr dφ B) r dr dφ C) r2 dr dφ D) dx dy
A) 1 B) r C) φ D) r2
A) √π B) 1 C) 2π D) π
A) (0, 0, 1) B) (-sin φ, cos φ) C) (cos φ, sin φ) D) (r cos φ, r sin φ)
A) (cos φ, sin φ) B) (-sin φ, cos φ) C) (r, φ) D) (sin φ, -cos φ)
A) r̂ + φ̂ B) φ̂ × r̂ C) v̂ × r̂ D) r̂ × φ̂
A) r r̂ + φ φ̂ B) ṙ r̂ + rφ̇ φ̂ C) ṙ r̂ + φ̇ φ̂ D) ṙ φ̂ + rφ̇ r̂
A) revolutions per second B) radians per second C) degrees per second D) meters per second
A) r̈ B) r̈ + rφ̇2 C) rφ̈ + 2ṙφ̇ D) r̈ - rφ̇2
A) rφ̈ + 2ṙφ̇ B) 2ṙφ̇ C) r̈ - rφ̇2 D) rφ̈
A) r * (d/dt)(r φ̇2) B) (1/r) * (d/dt)(r2 φ̇) C) r2 * φ̈ D) (d/dt)(r2 φ̇)
A) (dr/dθ)êr + (dr/dθ)êθ B) r êθ C) r êr + (dr/dθ)êθ D) (dr/dθ)êr + r êθ
A) (d2r/dθ2)êr + 2(dr/dθ)êθ B) (d2r/dθ2)êr + (dr/dθ)êθ C) (d2r/dθ2 - r)êr + r êθ D) (d2r/dθ2 - r)êr + 2(dr/dθ)êθ
A) r B) ρ C) θ D) φ
A) radians B) arcminutes C) gradians D) degrees
A) horizontally to the right B) horizontally to the left C) vertically downwards D) vertically upwards
A) vertically downwards B) horizontally to the right C) horizontally to the left D) vertically upwards
A) (-r, φ) B) (r, φ + 360°) C) (-r, φ + 180°) D) (r, φ + 180°)
A) The point is reflected B) The point remains the same C) The point moves to the pole D) The radius becomes negative
A) It cannot be represented B) (0, φ) for any φ C) (1, φ) for any φ D) (r, 0) for any r
A) [0, 180°) B) [0, 90°] C) [0, 720°) D) [0, 360°)
A) sin(x/y) B) cos(y/x) C) arctan(x, y) D) atan2(y, x)
A) Two distances B) An x-value and a y-value C) A distance and an angle D) Two angles
A) The origin point B) The radial point C) The center axis D) The pole
A) The radial line B) The angular axis C) The azimuth ray D) The polar axis
A) Chord B) Radius C) Polar angle D) Azimuth
A) Radial distance B) Linear distance C) Azimuth D) Pole coordinate
A) Bipolar B) Spherical C) Cartesian D) Cylindrical
A) Cubes B) Spirals C) Rectangles D) Squares
A) Grégoire de Saint-Vincent B) Gregorio Fontana C) Jacob Bernoulli D) Isaac Newton
A) Solving spherical trigonometry B) The study of circular and orbital motion C) Calculating parabolic arcs D) Mapping the Earth
A) Archimedes B) Pythagoras C) Hipparchus D) Euclid
A) Acta Eruditorum B) Method of Fluxions C) Origin of Polar Coordinates D) On Spirals
A) Julian Lowell Coolidge B) Alexis Clairaut C) Leonhard Euler D) George Peacock
A) Blaise Pascal B) Isaac Newton C) Jacob Bernoulli D) Bonaventura Cavalieri
A) Gregorio Fontana B) Blaise Pascal C) Grégoire de Saint-Vincent D) Hipparchus
A) On Spirals B) Differential and Integral Calculus C) Method of Fluxions D) Acta Eruditorum
A) Alexis Clairaut B) Isaac Newton C) Jacob Bernoulli D) Bonaventura Cavalieri
A) Alexis Clairaut B) Isaac Newton C) Leonhard Euler D) Jacob Bernoulli
A) Semi-latus rectum B) Argument C) Magnitude or modulus D) Eccentricity
A) Modulus B) Magnitude C) Argument D) Semi-latus rectum
A) Quadratic formula B) Pythagorean theorem C) Euler's formula D) De Moivre's formula
A) Multiplication B) Variable assignment C) Subtraction D) Addition
A) Euler's formula B) De Moivre's formula C) Archimedean formula D) Polar rose theorem
A) y B) φ C) x D) r
A) The diagonal B) The pole C) Vertical (90°/270°) ray D) Horizontal (0°/180°) ray
A) Eccentricity B) Magnitude C) Argument D) Radius
A) Circle B) Ellipse C) Hyperbola D) Parabola
A) Hyperbola B) Ellipse C) Circle D) Parabola
A) Ellipse B) Parabola C) Hyperbola D) Circle
A) Parabola B) Circle C) Hyperbola D) Ellipse
A) Trapezoid B) Pentagon C) Lemniscate D) Square
A) φ = r + γ B) r = γ C) φ = γ D) r = φ + γ
A) γ = cos(m) B) γ = arctan(m) C) γ = m2 D) γ = sin(m)
A) k/2 petals B) k petals C) k + 1 petals D) 2k petals
A) k + 2 petals B) k petals C) k/2 petals D) 2k petals
A) 4 B) 3 C) 6 D) 8
A) Constant distance B) Spatial frequency C) Amplitude D) Phase
A) It becomes a perfect circle B) A rose-like shape forms with overlapping petals C) No shape forms D) It becomes an Archimedean spiral
A) No, they represent completely different shapes B) Yes, they represent the same curve C) No, they differ by a rotation D) Yes, they are identical
A) Planisphere B) Polarimeter C) Planimetric compass D) Planimeter
A) Gauss's theorem B) Stokes' theorem C) Green's theorem D) Pythagorean theorem
A) Centrifugal force B) Angular velocity C) Centripetal acceleration D) Coriolis acceleration
A) Radial acceleration B) Centripetal acceleration C) Angular acceleration D) Coriolis acceleration
A) Everywhere in space B) Only in the inertial frame C) Only in the rotating frame D) Only at the origin
A) Tangentially counter-clockwise B) Tangentially clockwise C) Radially outward D) Radially inward
A) Opposite to Ω B) Decreasing r C) Increasing r D) Increasing φ
A) Only in three dimensions B) Yes C) Only at the origin D) No
A) Cylindrical B) Cartesian C) Latitude-longitude D) Spherical
A) ρ B) φ C) z D) δ
A) Hyperbola B) Parabola C) Ellipse D) Archimedean spiral
A) Clockwise B) Counterclockwise C) Eastward D) Upward
A) Magnetic west B) Magnetic east C) Magnetic north D) Magnetic south
A) Magnetic west B) Magnetic east C) Magnetic north D) Magnetic south
A) Nine-zero B) Ninety degrees C) Heading ninety D) Zero-niner-zero
A) Radial symmetry B) Rotational symmetry C) Axial symmetry D) Reflective symmetry
A) Constant velocity law B) Radial symmetry law C) Linear force law D) Inverse-square law
A) Solar panels B) Wind turbines C) Jet engines D) Radio antennas
A) Omnidirectional B) Dynamic C) Cardioid D) Condenser
A) It becomes more directional B) It shifts toward omnidirectionality C) It disappears D) It becomes a straight line |
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