University Physics (14th Edition)
14th Edition
ISBN: 9780133969290
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
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Chapter 9, Problem 9.55E
CALC A slender rod with length L has a mass per unit length that varies with distance from the left end, where x = 0, according to dm/dx = γx, where γ has units of kg/m2. (a) Calculate the total mass of the rod in terms of γ and L. (b) Use Eq. (9.20) to calculate the moment of inertia of the rod for an axis at the left end, perpendicular to the rod. Use the expression you derived in part (a) to express I in terms of M and L. How does your result compare to that for a uniform rod? Explain, (c) Repeat part (b) for an axis at the right end of the rod. How do the results for parts (b) and (c) compare? Explain.
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A 20cm radius turn-table is turning with a constant angular speed ω0=33rev/min . The turn-table has a moment of inertia I=5.0kg(cm)2 relative to the axis through its center. Call this central axis the z-axis. A piece of sticky gum with mass m=50g falls straight down on the turn-table and sticks at a distance of 10cm from the center.
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A 20cm radius turn-table is turning with a constant angular speed ω0=33rev/min . The turn-table has a moment of inertia I=5.0kg(cm)2 relative to the axis through its center. Call this central axis the z-axis. A piece of sticky gum with mass m=50g falls straight down on the turn-table and sticks at a distance of 10cm from the center.
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A slender uniform rod 100.00 cm long is used as a meter stick. Two parallel axes that are perpendicular to the rod are considered. The first axis passes through the 50-cm mark and the second axis passes through the 9-cm mark. What is the ratio of the moment of inertia through the second axis to the moment of inertia through the first axis?
Chapter 9 Solutions
University Physics (14th Edition)
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