A nautilus shell is a spiral which gets thicker as it goes around. This can be...
A nautilus shell is a spiral which gets thicker as it goes
around. This can be modeled as a hoop, with a density that varies
with respect to angle: λ(θ) = θ. If the “hoop” has a radius of
0.5m, find the moment of inertial for an axis of rotation that goes
through the center symmetrically.
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A nautilus shell is a spiral which gets thicker as it goes
around. This can be...
1 Moment of inertia of a solid uniform sphere around its axis of symmetry a) What...
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...
Consider a particle of mass mm that is revolving with angular speed ω around an axis....
Consider a particle of mass mm that is revolving with angular speed ω around an axis. The perpendicular distance from the particle to the axis is rr (Figure 1). Part A: Find the kinetic energy K of the rotating particle. Express your answer in terms of m r ω. part C:Find the moment of inertia IhoopIhoop of a hoop of radius rr and mass mm with respect to an axis perpendicular to the hoop and passing through its center. (Figure...
a cylinder of m=0.53 kg and radiuS 0.32 m can rotate around an axis through its...
a cylinder of m=0.53 kg and radiuS 0.32 m can rotate around an axis through its center. the cylinder moment of inertial is given by MR^2 /2. the cylinder is initially at rest. A force of 0.70 N is then applied tangentially at the edge of the cylinder. how many radians will the cylinder rotate through during the first 2.5 seconds that the force is applied
10*) The Sun has approximate radius 7×108 m, and rotates around its axis once every 27...
10*) The Sun has approximate radius 7×108 m, and rotates around
its axis once every 27 days. a) Find its angular velocity in rad/s,
and (assuming it is a uniform sphere) write a formula for its
angular momentum expressing it in terms of its mass M (you do not
need to substitute a value for M). b) Suppose the Sun were to
collapse to a neutron star, which is a much denser state, without
losing any mass and without being...
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, ML MR2 about center Thin rod about end ML Cylindrical hoop, MR2 about center Plane or slab, about center Solid sphere, about diameter 3MR2 Plane or slab, about edge Ma Spherical shell, about diameter MR2 4. Use the results on page 300 of the textbook to do the following: A...
Please answer that question ASAP 1. Consider a disc and hoop both of the same mass...
Please answer that question ASAP
1. Consider a disc and hoop both of the same mass M, radius R and thickness I. a) Explain why one of these objects has a larger moment of inertia (about an axis through the center of mass and perpendicular to the plane of the object) than the other. What effect does the thickness I have on the rotational inertia? b) Explain how the rotational inertia of the disc may be obtained by adding the...
Problem 7 A satellite consists two cylinders which can rotate relative to each other about the common axis of summetry. The rotation can be precisely controlled through a built-in motor. Both cyllind...
Problem 7 A satellite consists two cylinders which can rotate relative to each other about the common axis of summetry. The rotation can be precisely controlled through a built-in motor. Both cyllinders can be asuumed to be uniform; they have the same mass, m 10.0 kg, and the same radius 0.30 m. The top cylinder has attached to it two balls, each of which has mass 1.0kg and radius b 0.1 m. Each ball is fastened to the end of...
the list of equations to list are attached! thanks! 6. A playground merry-go-round, i.e., a horizontal...
the list of equations to list are attached! thanks!
6. A playground merry-go-round, i.e., a horizontal disc of radius 3 m that can rotate about a vertical axis through its center, is rotating at an angular speed 1/s (measured, as usual, in terms of radians). The moment of inertia of the merry-go-round with respect to that axis is 3000 kg m? A student of mass 80 kg is standing at the center of the merry-go-round. The student now walks outward...
4. Use Kepler's Second Law and the fact that L-fxp to determine at which points in...
4. Use Kepler's Second Law and the fact that L-fxp to determine at which points in an elliptical orbit around the Sun a planet has maximum and minimum speeds. (Section 13.5 will help.) 5. At the end of example 13.10, there's an "Evaluate" blurb about how inside the surface of the Earth the force of gravity varies proportionally to the distance from the center, and it makes reference to the next chapter. which is about oscillation. Model the motion of...
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...
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...
10*) The Sun has approximate radius 7×108 m, and rotates around
its axis once every 27 days. a) Find its angular velocity in rad/s,
and (assuming it is a uniform sphere) write a formula for its
angular momentum expressing it in terms of its mass M (you do not
need to substitute a value for M). b) Suppose the Sun were to
collapse to a neutron star, which is a much denser state, without
losing any mass and without being...
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, ML MR2 about center Thin rod about end ML Cylindrical hoop, MR2 about center Plane or slab, about center Solid sphere, about diameter 3MR2 Plane or slab, about edge Ma Spherical shell, about diameter MR2 4. Use the results on page 300 of the textbook to do the following: A...
Please answer that question ASAP
1. Consider a disc and hoop both of the same mass M, radius R and thickness I. a) Explain why one of these objects has a larger moment of inertia (about an axis through the center of mass and perpendicular to the plane of the object) than the other. What effect does the thickness I have on the rotational inertia? b) Explain how the rotational inertia of the disc may be obtained by adding the...
Problem 7 A satellite consists two cylinders which can rotate relative to each other about the common axis of summetry. The rotation can be precisely controlled through a built-in motor. Both cyllinders can be asuumed to be uniform; they have the same mass, m 10.0 kg, and the same radius 0.30 m. The top cylinder has attached to it two balls, each of which has mass 1.0kg and radius b 0.1 m. Each ball is fastened to the end of...
the list of equations to list are attached! thanks!
6. A playground merry-go-round, i.e., a horizontal disc of radius 3 m that can rotate about a vertical axis through its center, is rotating at an angular speed 1/s (measured, as usual, in terms of radians). The moment of inertia of the merry-go-round with respect to that axis is 3000 kg m? A student of mass 80 kg is standing at the center of the merry-go-round. The student now walks outward...
4. Use Kepler's Second Law and the fact that L-fxp to determine at which points in an elliptical orbit around the Sun a planet has maximum and minimum speeds. (Section 13.5 will help.) 5. At the end of example 13.10, there's an "Evaluate" blurb about how inside the surface of the Earth the force of gravity varies proportionally to the distance from the center, and it makes reference to the next chapter. which is about oscillation. Model the motion of...
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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