A crucial part of a piece of machinery starts as a flat uniform cylindrical disk of radius R0 and mass M. It then has a circular hole of radius R1 drilled into it, see the figure.(Figure 1) The hole's center is a distance h from the center of the disk.
1. Find the moment of inertia of this disk (with off-center hole) when rotated about its center, C. [Hint: Consider a solid disk and "subtract" the hole; use the parallel-axis theorem.]
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A crucial part of a piece of machinery starts as a flat uniform
cylindrical disk of...
RO O A crucial part of a piece of machinery starts as a flat uniform cylindrical...
RO O A crucial part of a piece of machinery starts as a flat uniform cylindrical disk of radius Ro = 0.46 m and mass M = 22.68 kg. It then has a circular hole of radius R1 = 0.08 m drilled into it. The hole's center is a distance h = 0.08 m from the center of the disk. Find the moment of inertia of this disk (with off-center hole) when rotated about its center, in kg m².
A uniform disk with mass M and radius R is rotating about an axis through its center-of-mass.
A uniform disk with mass M and radius R is rotating about an axis through its center-of-mass. The axis is perpendicular to the disk. The moment of inertial for the disk with a central axis is I MR2. Two non-rotating smaller disks, each with mass M2 and radius R/4, are glued on the original disk as shown in the figure. (a) Show that the ratio of the moments of inertia is given by I'/I = 35/16, where I' is the moment...
Results given on page 300: TABLE 12.2 Moments of inertia of objects with uniform density Object...
Results given on page 300: TABLE 12.2 Moments of inertia of objects with uniform density Object and axis Picture Picture Object and axis Thin rod about center ML2 Cylinder or disk MR about center Thin rod about end ML Cylindrical hoop, MR2 about center Plane or slab, about center Маг | Solid sphere, about diameter MR2 Plane or slab about edge MaSpherical shell, about diameter MR2 2. b. A very thin, flat, uniform slab has a width of W, a...
Results given on page 300 TABLE 12.2 Moments of inertia of objects with uniform density Object...
Results given on page 300 TABLE 12.2 Moments of inertia of objects with uniform density Object and axis Picture Object and axis Picture Thin rod, about center | Cylinder or disk, about center MR ML2 Thin rod, about end ML Cylindrical hoop. MR2 about center | Solid sphere, about diameter Маг Plane or slab, about center Ma2 MR Plane or slab, about edge Ma2 Spherical shell, about diameter MR2 1. b. A very thin, straight, uniform rod has a length...
A box of mass m is released from rest on a frictionless slope as depicted on the left...
A box of mass m is released from rest on a frictionless slope as depicted on the left of the figure below. The slope is at an angle theta. From this information, calculate the acceleration of the box as it slides down the ramp. Next consider a uniform solid cylinder of radius R placed on a slope with the same angle theta as shown on the right of the figure above. When the cylinder is released from rest, it rolls without slip down the ramp. Calculate the acceleration...
Let's investigate the motion of a uniform cylinder (think of a checker piece rolling along its...
Let's investigate the motion of a uniform cylinder (think of a checker piece rolling along its circular edge) with radius released from a height h so that it makes it through a circular loop. It rolls down the hill, enters the loop of radius T_loop as shown, and never loses contact with the circular track. (Figure 1) We will assume the cylinder rolls without slipping. The cylinder's radius T_cyl is much smaller than the loop's radius T_loop Suppose we compare...
17. A parallel-plate, air-filled capacitor is being charged as in the Figure below The circular plates...
17. A parallel-plate, air-filled capacitor is being charged as in the Figure below The circular plates have radius 4.00 cm, and at a particular instant, the conduction current in the wires is o.720 A. Recall that the conduction current for the flat surface is equal to the displacement current for the curved bulging surface. Using Ampere's law, the magnitude of the magnetic field at point a distant by r 1 cm from the horizontal axis of two plates is: (5...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
RO O A crucial part of a piece of machinery starts as a flat uniform cylindrical disk of radius Ro = 0.46 m and mass M = 22.68 kg. It then has a circular hole of radius R1 = 0.08 m drilled into it. The hole's center is a distance h = 0.08 m from the center of the disk. Find the moment of inertia of this disk (with off-center hole) when rotated about its center, in kg m².
Results given on page 300: TABLE 12.2 Moments of inertia of objects with uniform density Object and axis Picture Picture Object and axis Thin rod about center ML2 Cylinder or disk MR about center Thin rod about end ML Cylindrical hoop, MR2 about center Plane or slab, about center Маг | Solid sphere, about diameter MR2 Plane or slab about edge MaSpherical shell, about diameter MR2 2. b. A very thin, flat, uniform slab has a width of W, a...
Results given on page 300 TABLE 12.2 Moments of inertia of objects with uniform density Object and axis Picture Object and axis Picture Thin rod, about center | Cylinder or disk, about center MR ML2 Thin rod, about end ML Cylindrical hoop. MR2 about center | Solid sphere, about diameter Маг Plane or slab, about center Ma2 MR Plane or slab, about edge Ma2 Spherical shell, about diameter MR2 1. b. A very thin, straight, uniform rod has a length...
A box of mass m is released from rest on a frictionless slope as depicted on the left of the figure below. The slope is at an angle theta. From this information, calculate the acceleration of the box as it slides down the ramp. Next consider a uniform solid cylinder of radius R placed on a slope with the same angle theta as shown on the right of the figure above. When the cylinder is released from rest, it rolls without slip down the ramp. Calculate the acceleration...
Let's investigate the motion of a uniform cylinder (think of a checker piece rolling along its circular edge) with radius released from a height h so that it makes it through a circular loop. It rolls down the hill, enters the loop of radius T_loop as shown, and never loses contact with the circular track. (Figure 1) We will assume the cylinder rolls without slipping. The cylinder's radius T_cyl is much smaller than the loop's radius T_loop Suppose we compare...
17. A parallel-plate, air-filled capacitor is being charged as in the Figure below The circular plates have radius 4.00 cm, and at a particular instant, the conduction current in the wires is o.720 A. Recall that the conduction current for the flat surface is equal to the displacement current for the curved bulging surface. Using Ampere's law, the magnitude of the magnetic field at point a distant by r 1 cm from the horizontal axis of two plates is: (5...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
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