Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Textbook Question
Chapter 13, Problem 63P
A solid cylinder of mass M and radius R is mounted on an axle through its center. The axle is attached to a horizontal spring of constant k, and the cylinder rolls back and forth without slipping (Fig. 13.33). Write the statement of energy conservation for this system, and differentiate it to obtain an equation analogous to Equation 13.3 (see Problem 62). Comparing your result with Equation 13.3, determine the angular frequency of the motion.
FIGURE 13.33 Problem 63
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A door stopper spring is held at an angle from its equilibrium position and then released, and the angular velocity of the plastic end is given by the function:
w(t) = 3e-0.2t
cos(7t)
1. Find its angular acceleration function a (t).
2. Find its angular displacement function 0 (t), assuming 0 (0) = 0.
3. If the rotational motion is confined to the xy plane, what is the direction of the acceleration at t-0?
Justify your answers with your rationale and equations used.
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A solid cylinder of mass M and radius R is mounted to an axle through its center. The axle is attached to a horizontal spring of constant k, as shown in the figure. Initially the cylinder is at rest and the spring is un-stretched. The cylinder is then pulled a distance A and released. The cylinder rolls back and forth without slipping.
A) Determine the angular frequency ωfreq and period T of the simple harmonic motion of this spring-rolling mass system? Express your answer in terms of k and M.
B) Assume that we have the same spring and mass system, onlynow the cylinder is released from rest on a frictionless surface at a distance A from the equilibrium position. What is the period of the simple harmonic motion of this system? Express your answer in terms of k and M.
A door stopper spring is held at an angle from its equilibrium position and
then released, and the angular velocity of the plastic end is given by the
function:
w(t) = 3e-0.2t
cos(7t)
1. Find its angular acceleration function a (t).
2. Find its angular displacement function 0 (t), assuming 0 (0) = 0.
3. If the rotational motion is confined to the xy plane, what is the direction of
the acceleration at t-0?
Chapter 13 Solutions
Essential University Physics (3rd Edition)
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