Rolling: a Uniform Solid Sphere of Mass 1

question 89

Essay

Rolling: A uniform solid sphere of mass 1.5 kg and diameter 30.0 cm starts from rest and rolls without slipping down a 35° incline that is 7.0 m long.
(a) Calculate the linear speed of the center of the sphere when it reaches the bottom of the incline.
(b) Determine the angular speed of the sphere about its center at the bottom of the incline.
(c) Through what angle (in radians) does this sphere turn as it rolls down the incline?
(d) Does the linear speed in (a) depend on the radius or mass of the sphere? Does the angular speed in (b) depend on the radius or mass of the sphere?

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Definitions:

Project Variance

The difference between planned and actual project performance, often measured in terms of cost or time.

PERT Analysis

Stands for Program Evaluation and Review Technique, a method used in project management to analyze the tasks involved in completing a project, especially the time needed to complete each task.

Beta Distribution

A statistical distribution ranging from 0 to 1, often used in Bayesian analysis and project forecasting, representing a family of probabilities.

Project Management

The discipline of initiating, planning, executing, controlling, and closing the work of a team to achieve specific goals and meet specific success criteria within a specified time.