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What is euler's equation of motion in spherical polar coordinate?
Euler's equation of motion in spherical polar coordinates describes the dynamics of a rigid body rotating about a fixed point. It includes terms for the inertial forces, Coriolis forces, and centrifugal forces acting on the body. The equation is a vector equation that relates the angular acceleration of the body to the external torques acting on it.
How does a rigid body differ from an elastic body?
A rigid body does not deform under stress, maintaining its shape, while an elastic body can deform under stress but will return to its original shape once the stress is removed. Rigid bodies are idealized as having infinite stiffness, while elastic bodies have finite stiffness allowing for deformation.
Why does a rigid body has frequency?
A rigid body will have a natural frequency of vibration due to its mass and stiffness properties. When disturbed from its equilibrium position, the body will oscillate at this natural frequency. This frequency is determined by the body's physical characteristics and can be calculated using principles of dynamics.
What object is rigid?
A Rigid body is defined as a system of particles which does not deform.
Why does a spinning ice skater pull her arms close and extend them?
A skater will pull his/her arms in close to their body while spinning to increase the speed and force of the spin in routines this also helps to improve the fluency of the routine and is able to keep going in time to the music. They extend their arms to improve the look of the spin within a performance or routine hope this answered your question :)
What is the moment of inertia about the instantaneous center in a rotating rigid body?
The moment of inertia about the instantaneous center in a rotating rigid body is a measure of how difficult it is to change the body's rotational motion around that point. It depends on the mass distribution and shape of the body.
What is inertia torque?
Inertia torque an imaginary torque, which when applied upon a rigid body, brings it in an equilibrium position. Its magnitude is equal to accelerating couple, but opposite in direction.T1 = -IαwhereI = mass moment of inertia of body andα = angular acceleration
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 moment of inertia about an axis of rotation body?
The moment of inertia of a body about an axis of rotation is a measure of its resistance to rotational motion. It depends on the mass of the body and how that mass is distributed around the axis of rotation. A body with a larger moment of inertia requires more torque to rotate at the same rate as a body with a smaller moment of inertia.
Relation between stress and moment of inertia?
is a resisstance of a body is called inertia
If moment of inertia of a body change of axis of rotation?
If the moment of inertia of a body changes due to a change of axis of rotation, the new moment of inertia can be calculated using the parallel axis theorem. This theorem states that the moment of inertia about a new axis parallel to the original axis can be found by adding the mass of the body multiplied by the square of the distance between the two axes.
What increase the moment of inertia?
A rotating body that spins about an external or internal axis (either fixed or unfixed) increase the moment of inertia.
Can one body have any number of moment of inertia?
It depends upon the velocity with which the object is travelling.... Higher the velocity, higher will be the moment of inertia.....
What is instantaneous centre of rotation?
The instantaneous center of rotation is a point in a rigid body that has zero velocity at a specific moment in time. It is the point around which all parts of the rigid body have rotation at that moment. It helps to analyze the motion of the rigid body at that instant.
What is the difference between mass moment of inertia and area moment of inertia?
Mass moment of inertia measures an object's resistance to rotational motion due to its mass distribution, while area moment of inertia measures an object's resistance to bending due to its shape and cross-sectional area. Mass moment of inertia depends on both the mass and its distribution, while area moment of inertia depends on the shape and how the material is distributed in the cross-section.
What is parallel axis theorem?
The parallel axis theorem is a principle in physics and engineering that allows the calculation of the moment of inertia of a rigid body about any axis parallel to an axis through its center of mass. It states that the moment of inertia ( I ) about the new axis is equal to the moment of inertia ( I_{cm} ) about the center of mass axis plus the product of the mass ( m ) of the body and the square of the distance ( d ) between the two axes: ( I = I_{cm} + md^2 ). This theorem is particularly useful in rotational dynamics for analyzing systems with complex shapes.
What variables contribute to moment of inertia?
The axis about which the body is being rotated and the geometry of the body are important. The further away material (in terms of area) is from the centroid of the body the higher the moment of inertia will be, which is why an I-beam is good in bending. If it's the mass moment of inertia which is used in dynamics for Euler's angular momentum equation. Then the mass of the body is important. The further away mass is from the axis of rotation the greater the mass moment of inertia will be. This is why when a figure skater pulls their arms into her body during a spin she begins to spin faster. The mass of their arms is now closer to their axis of rotation lowering their mass moment of inertia and decreasing their resistance to rotation.
