Use equation I=∫r2dm to calculate the moment of inertia of a uniform, hollow sphere with mass M and radius R for an axis passing through one of its diameters. Express your answer in terms of the variables M and R.
Use equation I=∫r2dm to calculate the moment of inertia of a uniform, solid cone with mass M, radius R and height H for its axis of symmetry. Express your answer in terms of the variables M and R.
Use equation I=∫r2dm to calculate the moment of inertia of a uniform, hollow sphere with mass M and radius R for an axis...
A hollow sphere and uniform sphere of the same mass m and radius R roll down an inclined plane from the same height H without slipping (Figure 9-59). Each is moving horizontally as it leaves the ramp. When the spheres | hit the ground, the range of the hollow sphere is L. Find the range L' of the uniform sphere. FIGURE Uniform Hollow sphere sphere
A uniform solid sphere has a moment of inertia I about an axis tangent to its surface. What is the moment of inertia of this sphere about an axis through its center?
Find the moment of inertia of a solid sphere (mass M, radius R) around a diameter. Do this by slicing the sphere into disks.
Find the moment of inertia of a solid sphere (mass M, radius R) around a diameter. Do this by slicing the sphere into disks.
Review A disk of mass M and radius R has a hole of radius centered on the axis. Part A Calculate the moment of inertia of the disk. Express your answer in terms of the variables M, R, and T. VALD O2 ? MR2 mR 22 Submit Previous Answers Request Answer Part B A 5.0-cm-diameter disk with a 3.0-cm-diameter hole rolls down a 55-cm-long, 21 ° ramp. What is its speed at the bottom? Express your answer to two significant...
Problem 4. A solid sphere of mass m and radius r rolls without slipping along the track shown below. It starts from rest with the lowest point of the sphere at height h 3R above the bottom of the loop of radius R, much larger than r. Point P is on the track and it is R above the bottom of the loop. The moment of inertia of the ball about an axis through its center is I-2/S mr. The...
n Given that the moment of inertia about a diameter of a uniform hollow thin spherical shell of mass m and radius r is jmr2. Show that the moment of inertia about a diameter of a non-uniform sphere of radius R with the volume mass density distribution given by por) (1-), where r denotes the radial distance from the center, is 1 MR2. (Hint: Imagine the sphere is made of infinitely many layers of 15M 8TtR3 very thin concentric spherical...
Lab 8 Assignment: Moment of Inertia 1) Moment of Inertia for Different Systems The resistance to rotational motion change is more involved than for linear motion because it not only depends on what the mass is, but also on how that mass is distributed about the axis of rotation. The farther away from the axis the mass is distributed, the greater the moment of inertia. Using this simple definition, for each of the following pairs of objects, determine which of...
1 Moment of inertia of a solid uniform sphere around its axis of symmetry a) What is the volume element dV of a sphere? b) Assume a constant density p MIV, calculate the moment of inertia, remember that r is measured from the rotation axis for each volume element Use the volume of a sphere to get a solution that only depends on the mass M and radius R of the sphere. c) 2) Spinning DVD On a DVD, data...
1. A solid sphere of radius R, mass M. and mo- ment of Inertia I = MR is rolling down a hill. It starts at rest at a height h. Find its speed at the bottom of the hill. Compare this to the speed an object of mass M would have after sliding down a frictionless hill also of height h.