Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 9, Problem 55P
To determine
To Find: Moment of inertia of a solidright circular cone.
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Prove that the moment of inertia of a solid sphere of uniform density, when rotating around a diameter,is 2MR2/5, where M is the mass of the sphere and R is the radius.Hint: integrate the infinitesimal volume element in spherical coordinates.
Prove that the moment of inertia of a solid cylinder of uniform density, when rotating around its central axis,is MR2/2, where M is the mass of the cylinder and R is its radius. Hint: integrate the infinitesimal volume element in cylindrical coordinates
Show that the moment of inertia of a right circular cone of mass M , height h and radius ‘a ’ about its axis is 3 Ma2/10. USE INTEGRATION.
Chapter 9 Solutions
Physics for Scientists and Engineers
Ch. 9 - Prob. 1PCh. 9 - Prob. 2PCh. 9 - Prob. 3PCh. 9 - Prob. 4PCh. 9 - Prob. 5PCh. 9 - Prob. 6PCh. 9 - Prob. 7PCh. 9 - Prob. 8PCh. 9 - Prob. 9PCh. 9 - Prob. 10P
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- If the angular acceleration of a rigid body is zero, what is the functional form of the angular velocity?arrow_forwardCan you assign an angular momentum to a particle without first defining a reference point?arrow_forwardA uniform rod of length b stands vertically upright on a rough floor and then tips over. What is the rods angular velocity when it hits the floor?arrow_forward
- A rigid body with a cylindrical cross-section is released from the top of a 30 incline. It rolls 10.0 m to the bottom in 2.60 s. Find the moment of inertia of the body In terms of its mass m and radius r.arrow_forwardUsing the parallel axis theorem, what is the moment of inertia of the rod of mass m about the axis shown below?arrow_forwardA solid cylinder of mass 2.0 kg and radius 20 cm is rotating counterclockwise around a vertical axis through its center at 600 rev/min. A second solid cylinder of the same mass and radius is rotating clockwise around the same vertical axis at 900 rev/min. If the cylinders couple so that they rotate about the same vertical axis, what is the angular velocity of the combination?arrow_forward
- If the torque acting on a particle about an axis through a certain origin is zero, what can you say about its angular momentum about that axis?arrow_forwardCheck Your Understanding What is the moment of inertia of a cylinder of radius R and mass m about an axis through a point on the surface, as shown below? A uniform thin disk about an axis through the center Integrating to find the moment of inertia of a two-dimensional object is a little bit trickier, but one shape is commonly done at this level of study—a uniform thin disk about an axis through its center (Figure 10.27). Figure 10.27 Calculating the moment of inertia for a thin disk about an axis through its center.arrow_forwardA wheel 2.00 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 4.00 rad/s2. The wheel starts at rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.3 with the horizontal at this time. At t = 2.00 s, find (a) the angular speed of the wheel and, for point P, (b) the tangential speed, (c) the total acceleration, and (d) the angular position.arrow_forward
- Find the moment of inertia of the rod in the previous problem by direct integration.arrow_forwardCalculate the moment of inertia by direct integration of a thin rod of mass M and length L about an axis through the rod L/3 , as shown below. Check your answer with the parallel-axis theorem.arrow_forwardIf you know the velocity of a particle, can you say anything about the particle’s angular momentum?arrow_forward
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