What is Solid sphere: Definition and 100 Discussions

In mathematics, a ball is the volume space bounded by a sphere; it is also called a solid sphere. It may be a closed ball (including the boundary points that constitute the sphere) or an open ball (excluding them).
These concepts are defined not only in three-dimensional Euclidean space but also for lower and higher dimensions, and for metric spaces in general. A ball or hyperball in n dimensions is called an n-ball and is bounded by an (n − 1)-sphere. Thus, for example, a ball in the Euclidean plane is the same thing as a disk, the area bounded by a circle. In Euclidean 3-space, a ball is taken to be the volume bounded by a 2-dimensional sphere. In a one-dimensional space, a ball is a line segment.
In other contexts, such as in Euclidean geometry and informal use, sphere is sometimes used to mean ball.

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  1. S

    Determining the total distance a solid sphere will roll.

    Hi guys. I'm trying to calculate the total distance a marble (I'm modeling it as non-deformable solid sphere) will travel along a flat cardboard surface (I'm also assuming the cardboard does not deform). The sphere will initially be propelled by a known external force, it can be assumed that...
  2. S

    Determining the total distance a solid sphere will roll.

    Hi guys not sure if this belongs in the homework section, anyway here goes! I'm trying to calculate the total distance a marble (I'm modeling it as non-deformable solid sphere) will travel along a flat cardboard surface (I'm also assuming the cardboard does not deform). The sphere will...
  3. F

    Electromagnetic fields of a rotating solid sphere: total charge inside

    Homework Statement A solid sphere of radius a rotates with angular velocity ω\hat{z} relative to an inertial frame K in which the sphere's center is at rest. In a frame K' located at the surface of the sphere, there is no electric field, and the magnetic field is a dipole field with M=M\hat{z}...
  4. lonewolf219

    Can Gauss' Law Be Applied to a Non-Uniformly Charged Solid Sphere?

    Question: A solid sphere of radius R has a non-uniform charge distribution of p=Ar^2, where A is constant. Find total charge Q within the volume of the sphere. p=roe p=Q/dV EdA=qenclosed/Enaught Can you use Gauss' Law for this problem when sphere is solid? If so, how? Since p...
  5. D

    Calculating Gravity Inside Complex Spherical Bodies

    I know about the shell theorem and that the force of gravity due to the mass of the shell is zero inside a spherical shell. I have some questions that may easily be answered. 1. Does this same conclusion hold for an ellipsoid and/or a disk with the shell on the exterior rim ? 2. How is...
  6. P

    Moment of inertia of a solid sphere derivation.

    Hello! I'm trying to derive the formula for the moment of inertia of a solid sphere, and I keep running into a strange solution. I set up the infinitesimally mass of an infinitesimally thin "shell" of the sphere: dm = 4\rho\pir2 dr And then solved for the moment of inertia: I = \intr2dm =...
  7. K

    Rotational motion of a solid sphere of mass

    A solid sphere of mass m is released from rest from the rim of a hemispherical cup so that it rolls along the surface. If the rim of the hemisphere is kept horizontal, find the normal force exerted by the cup on the ball when the ball reaches the bottom of the cup.
  8. M

    Uniform Solid Sphere Moment of Inertia Calculation

    Find the moment of inertia of a uniform solid sphere of mass,m and radius,a about an axis through its centre. I have tried to solve it but I get the different answer, I don't know where I have done mistake. Please! check and correct my solution below:- Consider a volume element, dv of the...
  9. J

    Angular acceleration of solid sphere on frictionless yoke unde no slip roll condition

    Homework Statement m=6kg r=0.18m Fapp=33N I'm struggling to understand how to answer this question and correlate the linear force applied to rotation without being given the coefficient of friction causing the rotational motion. The question states that a solid sphere of 6kg is...
  10. E

    Electric field, solid sphere inside hollow sphere

    Homework Statement basically, my question is this, in relation to this diagram, https://www.physicsforums.com/attachment.php?attachmentid=12482&d=1202140386 wouldn't the electric field between the solid sphere and the hollow sphere be a uniform field? Homework Equations The...
  11. G

    Electric Field of Nonconducting Solid Sphere

    Homework Statement A nonconducting solid sphere of radius 2.30 cm carries a uniformly distributed positive charge of 8.00×10-9 C. Calculate the magnitude of electric field at 1.60 cm away from the center of sphere Homework Equations E=kqr/R^3 The Attempt at a Solution...
  12. B

    The moment of inertia of a solid sphere

    Homework Statement A solid ball of mass M and radius is connected to a thin rod of mass m and length L as shown. What is the moment of inertia of this system about an axis perpendicular to the other end of the rod? Image: http://imageshack.us/photo/my-images/35/helpfy.jpg/ Homework...
  13. C

    Can a solid sphere only be considered a point for inverse-square forces?

    I am curious as to whether the force of solid sphere can be considered to be originating entirely at its center when the force is not of \frac{1}{r^2} nature. It is said that the field inside a uniform spherical shell is zero for any \frac{1}{r^2} type force and not for any others. It would...
  14. A

    What is the relation between a shell and a solid sphere?

    Homework Statement Homework Equations The Attempt at a Solution What is the relation between a shell and a solid sphere? Can you give me some hints?
  15. G

    Equation for a floating solid sphere

    Homework Statement A sphere is floating in water. It is pushed just under the water level and released. I'm asked to write the equation of motion for the sphere, not assuming small oscillations. Is it just: my''=\rho V g - mg ? Or do I have to include that the buoyant force is changing...
  16. L

    Question about charge density in a solid sphere

    I've already posted this question in the advanced physics forum, but I really think it should go here. My apologies for the double posting. Homework Statement If we are given a uniformly charged solid sphere with total charge Q and radius R, then the volume charge density rho is given by...
  17. P

    Solid sphere Kinetic Energy problem

    Homework Statement A solid sphere is released from rest at the top of an incline of height H and angle 30°. The sphere then rolls down the incline without slipping until it reaches the bottom of the incline, at which point the speed of the center-of-mass of the sphere is found to be 65 cm/s...
  18. K

    Potential Energy of a solid sphere and a thin disk

    A solid sphere with radius r is placed on top of a thin disk with radius R. The contact point is the center of the disk. Both objects are uniform and have the same mass M. Calculate the gravitational potential energy of the system. Take the potential energy to be zero when the sphere and the...
  19. A

    MoI of a Solid Sphere Derivation

    I'm aware of many, many solutions to this on the web (and on the forum) that I can follow, but I'm trying a different way (there are many, after all) and I can't figure out why it's not working, and I'd love to know where my logic is flawed. I have a solid sphere, and I'm splitting it up into...
  20. A

    Uniform solid sphere rolling on inclined plane

    Homework Statement A uniform solid sphere,rolls without slipping on a horizontal surface with an angular velocity \omega,meets a rough inclined plane of incination 60(degrees).The sphere starts pure rolling up the plane with an angular velocity.Find the new angular velocity . Homework...
  21. E

    Electric Potential inside insulating solid sphere.

    Homework Statement Hi everyone, I'm supposed to find an expression for the electric potential as a function of r, the radial distance inside a solid and non conducting sphere of radius R. A total charge of q is uniformly distributed throughout its volume. The annoying part is that I'm supposed...
  22. L

    Point charge inside solid sphere

    I'm curious. Say you have a solid, positively charged sphere with a uniform charge distribution. Now suppose you place a single, negatively charged electron inside the solid sphere. How will the electron behave? I assume the electrostatic forces exerted on the electron will ultimately tend it...
  23. M

    Uniform Electric Field in Cavity of Solid Sphere

    Homework Statement A charge q is uniformly distributed over the volume of a solid sphere of radius R. A spherical cavity is cut out of this solid sphere, and the material and its charges are discarded. Show that the electric field in the cavity will then be uniform, of magnitude...
  24. H

    Electric field inside a uniformly charged solid sphere .

    Homework Statement It is just a conceptual question. I learned that all charges tend to move toward outer surface, meaning all the charges of the solid sphere will be on the surface of the solid sphere. Then, why is it that the electric field increases linearly with distance? shouldn't it...
  25. N

    Moment of inertia of a solid sphere calculation

    How would one calculate the moment of inertia of a solid sphere (of uniform density, rotating about the axis through its center)? I know it's 2MR^{2}/5 but I got 3MR^{2}/5 when I attempted to derive it (just for fun, because I find rotational dynamics rather interesting). I would prefer a...
  26. U

    Moment of Inertia of Solid Sphere

    This is not homework, just my practise question for an exam. I keep getting an answer of 3/5MR^2 when the correct one is 2/5MR^2, and that was only because I fluked it by deciding to change my intergrand a little bit. I've some sources including one from hyperphysics which suggests...
  27. Q

    Moment of inertia of solid sphere

    Hi, i am trying to find the moment of inertia of a uniform density solid sphere about z-axis I = integrate => x^2 dm x = perpendicular distance from z-axis to anywhere in sphere so by pythagorus theorem, r^2 - z^2 = x^2 since dm = p dV and V = 4/3 (//pi)r^3 dV = 4(//pi)r^2 dr so I =...
  28. G

    Conservation of Angular Momentum of solid sphere

    Homework Statement A small solid sphere, with radius 0.25 cm and mass 0.61 g rolls without slipping on the inside of a large fixed hemisphere with radius 17 cm and a vertical axis of symmetry. The sphere starts at the top from rest. And I figured out that the KE at the bottom is = .001J...
  29. F

    Rotational Dynamics of a solid sphere

    Homework Statement A solid sphere starts from rest at the upper end of the track, as shown in figure below, and rolls without slipping until it rolls off the right-hand end. If H = 12.0 m and h = 2.0 m and the track is horizontal at the right-hand end, how far horizontally from point A does...
  30. I

    Solid sphere rolling on rough surface

    Hello ! Is there an expression for the friction force exerted on a solid sphere rolling (or rolling and slipping) on a rough solid inclined plane ? I have searched a lot but couldn't find anything, most studies are related to caoutchouc spheres or plane that will deform anbd cause viscoplastic...
  31. P

    Triple integral to find the gravity inside a solid sphere

    gravity inside a solid sphere Homework Statement I'm having a hard time setting up a triple integral to find the force of gravity inside a solid sphere. I've done a similar proof in physics before with gravity inside a spherical shell, but it only required a single integral. In this problem...
  32. F

    Find the electric field strength inside a solid sphere.

    Homework Statement A solid sphere 25cm in radius carries 14uC, distributed uniformly throughout its volume. Find the electric field strength (a.) 15cm, (b.) 25cm, (c.) 50cm from the sphere's center. R = .25m Q = 14 * 10^-6 C Homework Equations p = q/(volume) E = (kq)/r^2 The...
  33. F

    Calculating Particle Travel Time in Solid Sphere Under Gravity

    Homework Statement How would I go about finding the time it takes for a particle of mass m to travel in a straight line only under the force of gravity between any two points on the surface of a solid sphere of mass M. Homework Equations \mathbf{F}=-{3GM \over R^3} \matbhf{r} (I derived...
  34. B

    Solid sphere inside a hollow sphere.

    Question Details: The figure shows a solid metal sphere at the center of a hollow metal sphere. 1- What is the total charge on the exterior of the inner sphere? 2- What is the total charge on the inside surface of the hollow sphere? 3- What is the total charge on the exterior...
  35. S

    Electric Fields in Solid Sphere and Thick Shell

    Homework Statement What is the electric field at r1, r2, r3 for a solid sphere within a thick spherical shell where r1=1.5cm, r2=5.0cm, r3=8.0cm? The solid sphere has a total charge of 3C and the thick shell has a charge of -9C. a=2.0cm, b=4.0cm, c=6.0cm. (a=radius of solid sphere, b=inner...
  36. cepheid

    Moment of Inertia: Solid Sphere

    Hi, So as not to lead anybody astray, I have decided to post a correction to my ill-fated attempt in this thread: https://www.physicsforums.com/showthread.php?t=158832 to derive the moment of inertia of a solid sphere of uniform density and radius R. dI = r_{\perp}^{2} dm = r_{\perp}^{2}...
  37. S

    Force on a uniformly charged solid sphere

    Homework Statement Griffiths Example 8.2 Determine the net force on the northern hemisphere of a uniformly charged solid sphere of radius R and charge Q. use maxwell's stress tensor to calculate the force. (Not Gauss/Coulomb's law) Homework Equations The stress tensor is defined by...
  38. F

    Gravity inside a solid sphere.

    I'm trying to understand why there is no gravitational force on a mass inside a solid sphere. It's clear why the only force could be toward the centre of gravity, but my problem is this: Consider a point of mass halfway between the centre of the sphere and the outside (as in the diagram). It...
  39. E

    Solid sphere vs. disk ramp test and time difference.

    A solid sphere and a solid disk are released from rest at the top of the ramp. The inclination angle is theta to the horizontal and the vertical height of the ramp is h. Determine the time difference between the objects for them to read the bottom of the ramp. This is what I've solved...
  40. A

    A Solid Sphere Release From Rest at the top of a Ramp.

    Please help me with this question. Thank you. A 2.0 kg solid sphere (radius = 0.10m) is released from rest at the top of a ramp and allow to roll without slipping. The ramp is 0.75m high and 5.3 m long. Find Ktotal, Krot, and Ktranslation.
  41. A

    Moment of inertia of solid sphere

    Sometime back, I had quite some fun trying to derive the expressions for MOI of different rigid bodies using calculus. However, I had some trouble with the MOI of a solid sphere about an axis through its centre. The problem being that my final answer was markedly different from the original...
  42. A

    Moment of inertia of a uniform solid sphere

    Posted this question in the calculus section but I guess it's more of a basic physics question, so I've copied it here - Taking a uniform solid sphere of radius R and mass M, with the centre of mass at the origin, I divided it into infinitesimal disks of thickness dx, and radius y. I need to...
  43. A

    Moment of inertia of a uniform solid sphere

    This is not a homework question but I figured this was the most appropriate place to post it- Taking a uniform solid sphere of radius R and mass M, with the centre of mass at the origin, I divided it into infinitesimal disks of thickness dx, and radius y. I need to find the moment of inertia...
  44. P

    Calculating Electric Field of a Solid Sphere with Nonuniform Charge Density

    Consider a solid insulating sphere of radius b with nonuniform charge density \sigma = ar where a is a constant. Find the charge Q_r contained within the radius r, when r < b. Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4\pi r^2 . I got this...
  45. D

    Moment of inertia about center of solid sphere

    Here's the question: Show that the moment of inertia of a spherical shell of radius R and mass m is 2mR²/3. This can be done by direct integration or, more easily, by finding the increase in the moment of inertia of a solid sphere when its radius changes. To do this, first show that the moment...
  46. J

    Derivation of solid sphere moment of inertia

    I need to derive the moment of inertia for a solid sphere, but I'm having some trouble. I did the following. I=?r^2dm given density, p= m/V pV=m so pdV=dm and differentiating V wrt r, d(4/3?r^3)dr = 4?r^2 so p4?r^2dr=dm and plugging that in I get I=?r^2(p4?r^2)dr I pull the p4...
  47. R

    Vibrational Modes of a Solid Sphere

    Could someone please tell me how I could calculate the vibrational modes of a solid sphere, or where I could find this information? I want to make the calculations for a sphere with a unit radius.
  48. J

    What is the angular momentum of a spinning solid sphere

    What is the angular momentum of a spinning solid sphere of mass 'm', equitorial velocity 'v', and radius 'r'? (The mass of the sphere being uniformly distributed and the spin being along a single axis only) I can't figure this out because the common textbook formula for angular momentum...
  49. Norman

    Moment of Inertia for a Solid Sphere

    So I am having an issue getting the correct moment here. Although this isn't homework, I thought this would be the best forum for the issue. So... I=r^2dm Assuming a const mass density: I=p r^2 dV, (p=mass/volume). For a sphere the natural choice of dV = r^2 dr d(omega). So this leads...
  50. M

    How to Calculate Distance and Acceleration of a Rolling Sphere on a Ramp

    Hey there. My question is: A solid sphere of mass 2.5 kg and radius R =0.20 m is initially rolling along the horizontal without slipping with a center of mass speed V=6.0 m/s 1) if the sphere then rolls without slipping up a fixed ramp(25 deg) and a coefficient of static friction of...
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