The center of oscillation of a physical pendulum has this interesting property: It an impulse (assumed horizontal and in the plane of oscillation) acts at the center of oscillation, no oscillations are felt at the point of support. Baseball players (and players of many other sports) know that unless the ball hits the bat at this point (called the “sweet spot” by athletes), the oscillations due to the impact will sting their hands. To prove this property, let the stick in Fig. 15-I3 a simulate a baseball bat. Suppose that a horizontal force F → (due to impact with the ball) acts toward the right at P , the center of oscillation. The batter is assumed to hold the bat at O , the pivot point of the stick, (a) What acceleration does the point O undergo as a result of F → ? (b) What angular acceleration is produced by F → about the center of mass of the stick? (c) As a result of the angular acceleration in (b), what linear acceleration does point O undergo? (d) Considering the magnitudes and directions of the accelerations in (a) and (c), convince yourself that P is indeed the “sweet spot.”
The center of oscillation of a physical pendulum has this interesting property: It an impulse (assumed horizontal and in the plane of oscillation) acts at the center of oscillation, no oscillations are felt at the point of support. Baseball players (and players of many other sports) know that unless the ball hits the bat at this point (called the “sweet spot” by athletes), the oscillations due to the impact will sting their hands. To prove this property, let the stick in Fig. 15-I3 a simulate a baseball bat. Suppose that a horizontal force F → (due to impact with the ball) acts toward the right at P , the center of oscillation. The batter is assumed to hold the bat at O , the pivot point of the stick, (a) What acceleration does the point O undergo as a result of F → ? (b) What angular acceleration is produced by F → about the center of mass of the stick? (c) As a result of the angular acceleration in (b), what linear acceleration does point O undergo? (d) Considering the magnitudes and directions of the accelerations in (a) and (c), convince yourself that P is indeed the “sweet spot.”
The center of oscillation of a physical pendulum has this interesting property: It an impulse (assumed horizontal and in the plane of oscillation) acts at the center of oscillation, no oscillations are felt at the point of support. Baseball players (and players of many other sports) know that unless the ball hits the bat at this point (called the “sweet spot” by athletes), the oscillations due to the impact will sting their hands. To prove this property, let the stick in Fig. 15-I3a simulate a baseball bat. Suppose that a horizontal force
F
→
(due to impact with the ball) acts toward the right at P, the center of oscillation. The batter is assumed to hold the bat at O, the pivot point of the stick, (a) What acceleration does the point O undergo as a result of
F
→
? (b) What angular acceleration is produced by
F
→
about the center of mass of the stick? (c) As a result of the angular acceleration in (b), what linear acceleration does point O undergo? (d) Considering the magnitudes and directions of the accelerations in (a) and (c), convince yourself that P is indeed the “sweet spot.”
Study of body parts and their functions. In this combined field of study, anatomy refers to studying the body structure of organisms, whereas physiology refers to their function.
https://www.youtube.com/watch?v=6F6deDoKLoE
During the lab, you fire the ballistic pendulum multiple times and find the average angle to be 46.7 degrees.
If the length of the pendulum (from pivot to center of gravity) is 30.4 cm, to what height, h, did the pendulum's center of gravity rise?
(Use the formula shown at 7:45 of the video)
Give your answer in cm to 3 significant figures (2 decimal places in this case).
Discussing free vibrations and show that the frequency of oscillation for such a system is given by:
f
27 V m
A 22 g ball with a radius of 24 mm rolls back and forth in a hemispherical bowl of radius 7.5 cm. (a) What is the period of the oscillation if the ball is solid? (b) What is the period of the oscillation if the ball is hollow? (c) What is the percent difference between the two?
Glencoe Physics: Principles and Problems, Student Edition
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