On which of the following does the moment of inertia depend on?
The moment of inertia does not depend on the linear speed, linear acceleration, angular speed, and angular acceleration. However, it depends on the total mass. It depends on density and thus the shape of object. It also depends on the axis of rotation, by the virtue of r in the equation.
How does the moment of inertia affect the linear velocity of an object?
In the rotating system, the moment of inertia takes the role of the mass and the angular velocity takes the role of the linear velocity. Due to conservation of angular momentum this process transfers angular momentum to the Moon’s orbital motion, increasing its distance from Earth and its orbital period.
Does the radius of gyration depend on the angular velocity of the body?
The radius of gyration does not depend on the total mass of a body but depends upon the shape and size of body-distribution of mass within the body and choice of rotation of axis.
On what factors does radius of gyration depends on?
On what factors radius of gyration depends? Some of the factors that influence the value of the radius of gyration are the size and shape of the body, configuration of the rotational axis and position. It also depends on body mass distribution with respect to the rotational axis.
What does radius of gyration depends on?
The radius of gyration depends upon shape and size of the body, position and configuration of the axis of rotation, and also on the distribution of the mass of the body wrt the axis of rotation.
On what factors does radius of gyration of body depends?
The radius of gyration of a body depends on (i) position and orientation of the axis of rotation (ii) distribution of mass of the body about the axis of rotation. Find the centre of mass of three particle at the vertices of an equilateral triangle.
What is the dimension of radius of gyration?
So finally, the dimensional formula of the radius of gyration will be written as: [M0LT0]. The power of zero on the dimension of the mass and time shows that the mass and the time dimensions are zero for the radius of gyration. So, the correct answer is “Option C”.
Why is moment of inertia also called rotational inertia?
Moment of inertia is also called rotational inertia because it is a measure of the “resistence” of an object to be accelerated in its rotation. An object with a big moment of inertia is more difficult to increase/decrease its angular velocity (speed of rotation), than an object with a low moment of inertia.
What are the limitation of dimensional equation?
The method cannot be considered to derive composite relations. Examples s = ut + 1/2 at2 and 2as = v2 – u2. A formula containing trigonometric function, exponential function, and logarithmic function can not derive from it. The method cannot be used to derive the relationship between more than three quantities.
What are the limitation of dimensions?
Dimensional Analysis can’t derive relation or formula if a physical quantity depends upon more than three factors having dimensions. It can’t derive a formula containing trigonometric function, exponential function, and logarithmic function and it can’t derive a relation having more than one part in an equation.