put R= r
Find the center of mass of a hemisphere with radius r, whose density is uniform.
held. A solid sphere has a radius R. The top hemisphere carries a uniform charge density p while the lower hemisphere has a uniform charge density of -p. Find an approximate formula for the potential outside the sphere, valid at distances r >> R. A solid sphere has a radius R. The top hemisphere carries a uniform charge density p while the lower hemisphere has a uniform charge density of -p. Find an approximate formula for the potential outside the...
Consider a solid hemisphere of radius R, constant mass density ρ, and a total mass M. Calculate all elements of the inertia tensor (in terms of M and R) of the hemisphere for a reference frame with its origin at the center of the circular base of the hemisphere. Make sure to clearly sketch the hemisphere and axes positions.
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?
Question 4: Uniform charge Q is distributed in the volume of a hemisphere of radius R. Calculate the Electric field at the center of the sphere
Imagine a hypothetical star of radius R, whose mass density ρ is constant throughout the star. The star is composed of a classical ideal gas of ionized hydrogen, so there are free protons and free electrons flying around providing the pressure support. The star is in hydrostatic equilibrium (a) What is the pressure as a function of radius in the star, P(r)? As a boundary condition, the pressure at the surface should be zero, P(R) 0 (b) What is the...
A sphere of radius R,-0325 m and uniform charge density 645 3 lies at the center of a neutral, spherical, conducting shell of inner and outer radii R2- 0.533 m and Ro-0.815 m, respectively. Find the surface charge density on: The inner surface of the shell Number The outer surface of the shell Number pC/m2 R.
) 5. Show that the center of mass of a uniform semicircular plate of radius R is located at y = 4R/3π
Find the electric field at a distance r0 from the center of a spherical shell whose uniform surface charge density is σ and radius is R with R > r0
Problem 6a: A non-conducting thin shell in the shape of a hemisphere of radius R centered at the origin has a total charge Q spread uniformly over its surface. The hemisphere is oriented such that its base is in the (y.z) plane. al. Find an expression for the surface charge density η. a2. Find the electric field at the center of the hemisphere, i.e. at x-0. Hint: consider the hemisphere as a stack of rings