An object can possess kinetic energy in its translational motion and its rotation about its own axis. Furthermore, for a rolling object, the linear velocity and the angular velocity are related, through the objecť's radius. Moments of inertia of common objects have been calculated and tabulated (see your textbook for a small table, or Wikipedia for a larger one). For objects of circular geometry, this is some multiple of mR?, with m and R respectively the object's mass and radius. (for instance, a solid disk rotating like a wheel has I =mR?.) The kinetic energy of a rolling object consists of the translational and rotational terms: 1 1 K = mv². 1. Using the relationship between w and v for a rolling object, and moment of inertia I from a reference table, derive formulas for the kinetic energy in terms of the linear velocity v and mass m, for the following objects: a. Solid, uniform sphere b. Solid, uniform cylinder or disk c. Hollow, uniform sphere d. Uniform circular hoop

An object can possess kinetic energy in its translational motion and its rotation about its own axis. Furthermore, for a rolling object, the linear velocity and the angular velocity are related, through the objecť's radius. Moments of inertia of common objects have been calculated and tabulated (see your textbook for a small table, or Wikipedia for a larger one). For objects of circular geometry, this is some multiple of mR?, with m and R respectively the object's mass and radius. (for instance, a solid disk rotating like a wheel has I =mR?.) The kinetic energy of a rolling object consists of the translational and rotational terms: 1 1 K = mv². 1. Using the relationship between w and v for a rolling object, and moment of inertia I from a reference table, derive formulas for the kinetic energy in terms of the linear velocity v and mass m, for the following objects: a. Solid, uniform sphere b. Solid, uniform cylinder or disk c. Hollow, uniform sphere d. Uniform circular hoop

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Torque

Torque is the rotational equivalent of linear force in physics and mechanics. Based on the course of study, it is also known as the moment of force, rotational force, or turning effect.

Question

An object can possess kinetic energy in its translational motion and its rotation about its own axis.
Furthermore, for a rolling object, the linear velocity and the angular velocity are related, through the
objecť's radius.
Moments of inertia of common objects have been calculated and tabulated (see your textbook for a
small table, or Wikipedia for a larger one). For objects of circular geometry, this is some multiple of
mR?, with m and R respectively the object's mass and radius. (for instance, a solid disk rotating like a
wheel has I =mR2.)
The kinetic energy of a rolling object consists of the translational and rotational terms:
1
K =mv²
1
1. Using the relationship between w and v for a rolling object, and moment of inertia I from a
reference table, derive formulas for the kinetic energy in terms of the linear velocity v and mass
m, for the following objects:
a. Solid, uniform sphere
b. Solid, uniform cylinder or disk
c. Hollow, uniform sphere
d. Uniform circular hoop
2. In the figure at right, an object is placed at the top of
a ramp (point A) and allowed to roll downward to the
right. The ramp has a circular curvature of radius R,
centered on point P. At some point along the way
(point B in the diagram) the rolling object separates
from the ramp and falls freely until it reaches the
R
ground (point C).
For each of the four objects in part (1), determine the
angle o at which the object separates from the ramp. (Assume no energy loss to friction, air
drag, sound, etc.)

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