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"If a body be fastened to a string and whirled, so as to give it a circular motion, there will be a pull on the string that will be greater or less according as the velocity increases or decreases... If the string were cut, the pulling force that drew it away from the straight line would be removed, and the body would then fly off at a tangent; that is, it would move in a straight line tangent to the circle, as shown in Fig. 9." —Hallock 1905

Centrifugal Force

"If a body be fastened to a string and whirled, so as to give it a circular motion, there will be a…

"Attach a ball, for instance, to a cord; and , fastening the end of the cord at a point, O, give a quick impulse to the ball. It will be found to move in a circle, ABCD, because the cord keeps it within a certain distance of the centre (sic). Were it not for this, it would move in a straight line." —Quackenbos 1859

Centrifugal Force

"Attach a ball, for instance, to a cord; and , fastening the end of the cord at a point, O, give a quick…

"The instant one of the strings is let go, the centrifugal force carries off the stone in a tangent to the circle it was describing." —Quackenbos 1859

Centrifugal Force

"The instant one of the strings is let go, the centrifugal force carries off the stone in a tangent…

2 circles that are similar figures

Similar Figures

2 circles that are similar figures

Circle with diameter, radius, arc, chord, and arc.

Circle With Parts

Circle with diameter, radius, arc, chord, and arc.

Illustration of concentric circles.

Concentric Circles

Illustration of concentric circles.

Illustration of polygon inscribed in circle. Or, circle circumscribed about the polygon.

Polygon Inscribed in Circle

Illustration of polygon inscribed in circle. Or, circle circumscribed about the polygon.

Illustration of point of tangency (line and circle).

Point of Tangency

Illustration of point of tangency (line and circle).

Illustration of polygon circumscribed about circle. Or, circle inscribed in the polygon.

Polygon Circumscribed About Circle

Illustration of polygon circumscribed about circle. Or, circle inscribed in the polygon.

Illustration of circle with inscribed angle and central angle.

Inscribed and Central Angles

Illustration of circle with inscribed angle and central angle.

Illustration of circle with arc and chord.

Arc and Chord in Circle

Illustration of circle with arc and chord.

Illustration of circle with inscribed angle 30 and central angle 60.

Inscribed and Central Angles 30 60

Illustration of circle with inscribed angle 30 and central angle 60.

Illustration of radius drawn to point of contact of a tangent.

Point of Tangency

Illustration of radius drawn to point of contact of a tangent.

Illustration of circle with segments labeled and arch.

Segments of Circle and Arch

Illustration of circle with segments labeled and arch.

Illustration of circle with parts drawn to show area.

Area of a Circle by parts

Illustration of circle with parts drawn to show area.

Illustration of concentric circles used to find area between two circles (ring).

Concentric Circles (Ring) Area

Illustration of concentric circles used to find area between two circles (ring).

Illustration of circles used to find area between two circles (ring).

Area of Circles and Rings

Illustration of circles used to find area between two circles (ring).

Illustration of circle with sector and segment used to find area.

Circle With Sector and Segment labeled

Illustration of circle with sector and segment used to find area.

Illustration of partial circle with sector and segment used to find area.

Circle With Sector and Segment labeled

Illustration of partial circle with sector and segment used to find area.

Illustration of circle with diameter and segment used to find area.

Circle With Diameter and Segment labeled

Illustration of circle with diameter and segment used to find area.

Illustration of circle with 8 inch diameter.

Circle With 8 inch Diameter

Illustration of circle with 8 inch diameter.

Illustration of circle with 6 inch diameter.

Circle With 6 inch Diameter

Illustration of circle with 6 inch diameter.

Illustration of circle with 10 inch diameter and square.

Circle With 10 inch Diameter and Steel Square

Illustration of circle with 10 inch diameter and square.

Illustration of box filled with pipes.

Circular Pipes in Box

Illustration of box filled with pipes.

Illustration of three circles enclosed in an equilateral triangle.

Circles Enclosed in Equilateral Triangle

Illustration of three circles enclosed in an equilateral triangle.

Illustration of circle with radius of 4000, and triangle with 45 degree angle enclosed.

Circles With Radius 4000 and Enclosed Triangle

Illustration of circle with radius of 4000, and triangle with 45 degree angle enclosed.

Illustration of circle with arc, chord, diameter and radius.

Parts of Circle

Illustration of circle with arc, chord, diameter and radius.

Illustration of circle with quadrant and 60 degree arc.

Quadrant of Circle With 60 degree Arc

Illustration of circle with quadrant and 60 degree arc.

Illustration of circle with perpendicular diameters.

Circle With Perpendicular Diameters

Illustration of circle with perpendicular diameters.

Illustration of a wall with a rounded corner.

Corner of Rounded Wall

Illustration of a wall with a rounded corner.

Illustration of large circle and square with 4 smaller circles inside.

Circles Inside of a Square

Illustration of large circle and square with 4 smaller circles inside.

Illustration of ring (small circle in larger concentric circle).

Ring Made of Concentric Circles

Illustration of ring (small circle in larger concentric circle).

Illustration of ring (small circle in larger concentric circle) with piece cut out.

Ring With Piece Cut Out

Illustration of ring (small circle in larger concentric circle) with piece cut out.

Illustration of ring (small circle in larger concentric circle) sprung into place.

Ring Sprung Into Place

Illustration of ring (small circle in larger concentric circle) sprung into place.

Illustration of triangle inscribed in circle. Or, circle circumscribed about triangle.

Triangle Inscribed in Circle

Illustration of triangle inscribed in circle. Or, circle circumscribed about triangle.

Illustration of pentagon inscribed in circle. Or, circle circumscribed about pentagon.

Pentagon Inscribed in Circle

Illustration of pentagon inscribed in circle. Or, circle circumscribed about pentagon.

Illustration of hexagon inscribed in circle. Or, circle circumscribed about hexagon.

Hexagon Inscribed in Circle

Illustration of hexagon inscribed in circle. Or, circle circumscribed about hexagon.

Illustration of Circle with radian shown.

Circle With Radian

Illustration of Circle with radian shown.

Illustration of a circle with squares drawn to demonstrate area.

Area of Circle

Illustration of a circle with squares drawn to demonstrate area.

Circle divided into equal parts by concentric circles.

Dividing Circle into Equal Parts by Concentric

Circle divided into equal parts by concentric circles.

Illustration of circle with perpendicular diameters.

Circle With Perpendicular Diameters

Illustration of circle with perpendicular diameters.

Illustration of pentagon inscribed in circle. Or, circle circumscribed about pentagon. Construction lines shown.

Pentagon Inscribed in Circle by Construction

Illustration of pentagon inscribed in circle. Or, circle circumscribed about pentagon. Construction…

Illustration of regular hexagon and triangle inscribed in circle.

Hexagon Inscribed in Circle by Construction

Illustration of regular hexagon and triangle inscribed in circle.

Illustration of beginning of construction of a regular heptagon in a circle.

Construction of Regular Heptagon in a Circle

Illustration of beginning of construction of a regular heptagon in a circle.

Illustration of of construction of an arc when the chord and height of the segment are given.

Construction of Arc When Given the Chord and Height of the Segment

Illustration of of construction of an arc when the chord and height of the segment are given.

Illustration of of construction of a radius when given only a part of the circumference.

Construction of Radius When Given Only a Part of the Circumference

Illustration of of construction of a radius when given only a part of the circumference.

Illustration of of construction of a radius when given only a part of the circumference.

Construction of Radius When Given Only a Part of the Circumference

Illustration of of construction of a radius when given only a part of the circumference.

Right circular cylinder inscribed in a pentagonal prism. Or, Pentagonal prism circumscribed about a cylinder.

Cylinder Inscribed in Pentagonal Prism

Right circular cylinder inscribed in a pentagonal prism. Or, Pentagonal prism circumscribed about a…

Cross section of concrete conduit. The diagram can be used to find volume.

Cross Section of Concrete Conduit

Cross section of concrete conduit. The diagram can be used to find volume.

An illustration of a right circular cone with labels on slant height and altitude.

Right Circular Cone

An illustration of a right circular cone with labels on slant height and altitude.

An illustration of a circular cone.

Circular Cone

An illustration of a circular cone.

An illustration of a circular cone with the top cut off by a plane parallel to the base. The remaining part is called a frustum of a pyramid or a cone.

Circular Cone Frustum

An illustration of a circular cone with the top cut off by a plane parallel to the base. The remaining…

An illustration of a right circular cone with labels on slant height (12.422), radius (8), and altitude (12).

Right Circular Cone

An illustration of a right circular cone with labels on slant height (12.422), radius (8), and altitude…

An illustration of a right circular cone with labels on dimensions, and hole cut out. Illustration could be used for finding volume where subtraction is used.

Right Circular Cone With Hole Cut Out

An illustration of a right circular cone with labels on dimensions, and hole cut out. Illustration could…

An illustration of a right circular cone with altitude of 10 ft. and angle of 30 degrees.

Right Circular Cone 10 Feet High With 30 Degree Angle

An illustration of a right circular cone with altitude of 10 ft. and angle of 30 degrees.

An illustration of a sphere showing diameter, arcs, and circles. A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within, called the center.

Sphere with arcs and circles labeled.

An illustration of a sphere showing diameter, arcs, and circles. A sphere is a solid bounded by a curved…

An illustration of a sphere showing diameter, arcs, and circles. A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within, called the center. This shows the zones of a sphere.

Sphere With Arcs, Circles, and Zones Labeled.

An illustration of a sphere showing diameter, arcs, and circles. A sphere is a solid bounded by a curved…

An illustration of a sphere cut into polygons as bases with their vertices at the center of sphere.

Sphere Cut Into Pyramids.

An illustration of a sphere cut into polygons as bases with their vertices at the center of sphere.

An illustration of a sphere inside of a cylinder with radius/diameter labeled. Illustration for showing how volume is found.

Sphere Inside of Cylinder.

An illustration of a sphere inside of a cylinder with radius/diameter labeled. Illustration for showing…

An illustration of a zone of a sphere. A zone occurs when a sphere is cut by parallel planes that are equal distances apart. This illustration is the segment of one base.

Zones or Segments of Spheres

An illustration of a zone of a sphere. A zone occurs when a sphere is cut by parallel planes that are…