Concept explainers
The golden earring A disk of radius r is removed from a larger disk of radius R to form an earring (see figure). Assume the earring is a thin plate of uniform density.
a. Find the center of mass of the earring in terms of r and R. (Hint: Place the origin of a
b. Show that the ratio R/r such that the center of mass lies at the point P (on the edge of the inner disk) is the golden mean
(Source: P. Glaister, Golden Earrings, Mathematical Gazette, 80, 1996)
Want to see the full answer?
Check out a sample textbook solutionChapter 16 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Precalculus (10th Edition)
- Which lines or line segments or rays must be drawn or constructed in a triangle to locate its a orthocenter? b centroid?arrow_forwardDoes the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?arrow_forwardA storage shed is in the shape of a trapezoidal prism. Each trapezoid represents one of its bases. With dimensions as shown, what is the storage capacity volume of its interior?arrow_forward
- Which lines or line segments or rays must be drawn or constructed in a triangle to locate its aincenter? bCircumcenter? corthocenter? dcentroid?arrow_forwardFor compactness, the drop-down legs of an ironing board fold up under the board. A sliding mechanism at point A and the legs being connected at common midpoint M cause the boards upper surface to be parallel to the floor. How are AB and CD related?arrow_forwardFind the volume of the oblique circular cylinder. The axis meets the plane of the base to form a 45 angle.arrow_forward
- Find the exact volume of the solid that results when the triangular region with vertices at 0, 0, 6, 0 and 6, 4 is rotated about the a x-axis b y-axisarrow_forwardDoes a right circular cone such as a wizards cap have a symmetry with respect to at least one plane? b symmetry with respect to at least one line? c symmetry with respect to a point?arrow_forward
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
- Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL