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1. A solid uniform mass cone has its apex resting at (0,0,0) and is centered on...
3. 3D stuff. cylindrical coordinates. A cone of uniform mass density Po has its tip at...
3. 3D stuff. cylindrical coordinates. A cone of uniform mass density Po has its tip at the origin and its axis of symmetry is aligned with the z axis. The base of the cone is at H and has radius R. Draw a big picture! Compute the following things a. the total mass of the cone. b. the center of mass of the cone. c. its moment of inertia I2z around the z axis
Use equation I=∫r2dm to calculate the moment of inertia of a uniform, hollow sphere with mass M and radius R for an axis...
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.
M Two uniform, solid spheres (one has a mass M and a radius R and the...
M Two uniform, solid spheres (one has a mass M and a radius R and the other has a mass M and a radius R. = 2R) are connected by a thin, uniform rod of length L = 4R and mass M. Note that the figure may not be to scale. Find an expression for the moment of inertia I about the axis through the center of the rod. Write the expression in terms of M, R, and a numerical...
4. a) A solid truncated cone with smaller radius a and larger radius b, height h, and Determine the moment of inertia of the truncated cone in terms of a,b.p and central axis. 8 pts h when rotate...
4. a) A solid truncated cone with smaller radius a and larger radius b, height h, and Determine the moment of inertia of the truncated cone in terms of a,b.p and central axis. 8 pts h when rotated about its b) A bullet of with a mass-m,is fired into the cone with a speed v, in the z direction. The bullet a +b above the central axis of the cone and lodges in the cone at the enters the cone...
M Two uniform, solid spheres (one has a mass M and a radius R and the...
M Two uniform, solid spheres (one has a mass M and a radius R and the other has a mass M and a radius Rp = 2R) are connected by a thin, uniform rod of length L = 4R and mass M. Note that the figure may not be to scale. Find an expression for the moment of inertia / about the axis through the center of the rod. Write the expression in terms of M. R. and a numerical...
1. Consider a solid cone with uniform density p, height h, and circular base with radius R (hence mass M,sphR2). Let the vertex of the cone be the origin ofthe body frame. By symmetry, choose bas...
1. Consider a solid cone with uniform density p, height h, and circular base with radius R (hence mass M,sphR2). Let the vertex of the cone be the origin ofthe body frame. By symmetry, choose basis vectors e for the body frame such that the inertia tensor I, is diagonal. Will this rigid body with this body origin be an asymmetric top, a symmetric top, or a spherical top? Calculate the inertia tensor in this basis How will the inertia...
M 6 Two uniform, solid spheres (one has a mass M and a radius R and...
M 6 Two uniform, solid spheres (one has a mass M and a radius R and the other has a mass M and a radius Rp = 3R) are connected by a thin, uniform rod of length L = 4R and mass M. Note that the figure may not be to scale. Find an expression for the moment of inertia I about the axis through the center of the rod. Write the expression in terms of M, R, and a...
A solid cylinder of height L and radius R has uniform mass density . Find the...
A solid cylinder of height L and radius R has uniform mass density . Find the moment of inertia tensor about the center of the cylinder. For what value of L/R is the cylinder equally easy to spin about any axis?
Consider two right circular cones, cone A which is solid and cone B which is hollow...
Consider two right circular cones, cone A which is solid and cone B which is hollow and has mass only around the shell of the cone. Both cones have the same mass M , the same height H, and the same top radius R. Let the cone axes be along the y—axis with the tip at y=0 and the circular end at y=H. Which cone will have the largest moment of inertia?
two uniform solid spheres with mass M and radius R and the other with mass M...
two uniform solid spheres with
mass M and radius R and the other with mass M and radiius Rb =2R,
are connected by a thin uniform rod of length L=2R and mass M. find
an expression for the moment of inertia I about the axis through
the center of the rod. wrtie an expression in terms of M, R, and a
numerical factor in fraction form
Mandard and the chamad conected by a thirred of 2R and Find an expression...
3. 3D stuff. cylindrical coordinates. A cone of uniform mass density Po has its tip at the origin and its axis of symmetry is aligned with the z axis. The base of the cone is at H and has radius R. Draw a big picture! Compute the following things a. the total mass of the cone. b. the center of mass of the cone. c. its moment of inertia I2z around the z axis
M Two uniform, solid spheres (one has a mass M and a radius R and the other has a mass M and a radius R. = 2R) are connected by a thin, uniform rod of length L = 4R and mass M. Note that the figure may not be to scale. Find an expression for the moment of inertia I about the axis through the center of the rod. Write the expression in terms of M, R, and a numerical...
4. a) A solid truncated cone with smaller radius a and larger radius b, height h, and Determine the moment of inertia of the truncated cone in terms of a,b.p and central axis. 8 pts h when rotated about its b) A bullet of with a mass-m,is fired into the cone with a speed v, in the z direction. The bullet a +b above the central axis of the cone and lodges in the cone at the enters the cone...
M Two uniform, solid spheres (one has a mass M and a radius R and the other has a mass M and a radius Rp = 2R) are connected by a thin, uniform rod of length L = 4R and mass M. Note that the figure may not be to scale. Find an expression for the moment of inertia / about the axis through the center of the rod. Write the expression in terms of M. R. and a numerical...
1. Consider a solid cone with uniform density p, height h, and circular base with radius R (hence mass M,sphR2). Let the vertex of the cone be the origin ofthe body frame. By symmetry, choose basis vectors e for the body frame such that the inertia tensor I, is diagonal. Will this rigid body with this body origin be an asymmetric top, a symmetric top, or a spherical top? Calculate the inertia tensor in this basis How will the inertia...
M 6 Two uniform, solid spheres (one has a mass M and a radius R and the other has a mass M and a radius Rp = 3R) are connected by a thin, uniform rod of length L = 4R and mass M. Note that the figure may not be to scale. Find an expression for the moment of inertia I about the axis through the center of the rod. Write the expression in terms of M, R, and a...
two uniform solid spheres with
mass M and radius R and the other with mass M and radiius Rb =2R,
are connected by a thin uniform rod of length L=2R and mass M. find
an expression for the moment of inertia I about the axis through
the center of the rod. wrtie an expression in terms of M, R, and a
numerical factor in fraction form
Mandard and the chamad conected by a thirred of 2R and Find an expression...
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