0
Moment of inertia of a sphere How do you prove it using calculus As in deriving the equation using density and mass density being uniform?
The simple scalar method of calculation is to integrate the square of the radius (r) across dm, where m is the mass. (Integral r2 dm is the equation, but we don't have an integral sign here.) Use the link to Wikipedia for the rest of the information and expansions on the "basic" equation.
What else can I help you with?
When mercury water and air filled in three balls respectively qwhich has greater inertia?
Out of those substances, mercury has the greatest density. So for the same volume, mercury will be the heaviest and carry the most inertia.
What are words that describe the properties of mass?
* air pressure * and i dont know anymore lol sorry
How does thirty kilograms of paper clips and thirty five kilograms of lead compare in terms of mass and inertia?
The mass of thirty kilograms of paper clips is the same as thirty-five kilograms of lead. However, lead has a higher density than paper clips, so the lead will have a smaller volume compared to the paper clips. In terms of inertia, both objects will have the same inertia when experiencing the same acceleration, as inertia is directly proportional to mass.
If an objects velocity is doubled what happens to its inertia?
assuming its not starting at zero, if an object velocity is doubled, its kinetic energy (KE) is four times. If its trebled , its KE is nine times equation : KE = (m*v^2)/2 joules m=mass v=velocity
What is the tendency of an object to remain at rest or motion?
Inertia. Also described in Newton's First law of Motion.
What is the equation for calculating the polar moment of inertia of a cylinder?
The equation for calculating the polar moment of inertia of a cylinder is I ( r4) / 2, where I is the polar moment of inertia and r is the radius of the cylinder.
How can one determine the moments of inertia for a given object, and what methods are used in deriving moments of inertia?
To determine the moments of inertia for an object, one can use mathematical formulas or physical experiments. The moment of inertia depends on the shape and mass distribution of the object. Common methods for deriving moments of inertia include integration, parallel-axis theorem, and the perpendicular-axis theorem. These methods involve calculating the distribution of mass around an axis to determine how the object resists rotational motion.
How does the speed of a wave relate to the density of the medium it is traveling through?
The speed of a wave is inversely proportional to the square root of the density of the medium it is traveling through. As the density of the medium increases, the speed of the wave decreases. This relationship is described by the wave equation, which takes into account the elasticity and inertia of the medium.
Mass moment of inertia of a disk?
The mass moment of inertia of a disk is given by the equation I = (m * r^2) / 2, where m is the mass of the disk and r is the radius. This equation represents the resistance of the disk to rotational motion around its center.
What is the relationship between the moment of inertia times alpha in the context of rotational motion?
The relationship between the moment of inertia and angular acceleration (alpha) in rotational motion is described by the equation I, where represents the torque applied to an object, I is the moment of inertia, and is the angular acceleration. This equation shows that the torque applied to an object is directly proportional to its moment of inertia and angular acceleration.
How do you calculate the density of a metal ball without an overflow can or a graduated cylinder?
There are several methods that can be used to calculate the density of a metal ball. The density of a metal ball can be derived from the fact that the volume is: 4*(pi)*r^3/3 and the denisty is mass/volume. If the mass and moment of inertia are known but the dimensions of the metal ball are not, then you can use the fact that the moment of inertia of the ball is 2m*r^2/5 and solve for m to get r=(5I/2)^.5 and plug in the value for r into the volume equation then calculate the density of the ball by dividing the mass by the calculated volume.
What is the euler's equation of motion?
Euler's equation of motion relates the net torque acting on a rigid body to its angular acceleration and moment of inertia. It is expressed as: Στ = Iα, where Στ is the net torque acting on the body, I is the moment of inertia, and α is the angular acceleration.
What is the equation of torqe?
The net torque is equal to moment of inertia times angular acceleration. (Στ=Ia)
What is the torque acceleration equation used to calculate the rate of change of angular velocity in a rotating system?
The torque acceleration equation is used to calculate the rate of change of angular velocity in a rotating system. It is given by the formula: Torque Moment of Inertia x Angular Acceleration. This equation relates the torque applied to an object to its moment of inertia and the resulting angular acceleration.
What is the importance of integral calculus in engineering?
Its importance is tremendous - it has many different applications. Some of the applications include calculation of area, of volume, moment of inertia, of work, and many more.
How do you calculate inertia?
Inertia is the resistance of any object (in a physical state) to change pressed upon its current movement. It can be found by the Formula F=ma.F being force in relation to inertia, M being Mass, A is Acceleration.
Is mass a component of inertia?
Yes, mass is the only determining quality of inertia when referring to a one-dimensional case. However, if we're talking about rotation, there is a characteristic called "rotational inertia." Rotational inertia is calculated by, not only mass, but the distribution of total mass over a certain shape, in a certain orientation. Simple, common cases (such as flat disks, cylinders, spheres, etc...) can be described with neat equations, but most complex cases require calculus.
