state parellel and perpendicular axes theoren and write down their mathematical equations
Answers
Answer:
Suppose we want to calculate the moment of inertia of a uniform ring about its diameter. Let its centre be MR²/2, where M is the mass and R is the radius. So, by the theorem of perpendicular axes, IZ = Ix + Iy. Since the ring is uniform, all the diameters are equal.
I = moment of inertia of the body. Ic = moment of inertia about the centre. M = mass of the body. h2 = square of the distance between the two axes.
Explanation:
The parallel axis theorem states that, the moment of inertia of a body about any axis is equal to the moment of inertia about parallel axis through its center of mass plus the product of the mass of the body and the square of the perpendicular distance between the two parallel axes. .This is the parallel axis theorem.
Answer:
Hope this helps you
Explanation:
The parallel axis theorem states that
The moment of inertia of a body about an axis parallel to the body passing through its centre is equal to the sum of moment of inertia of the body about the axis passing through the centre and product of the mass of the body times the square of the distance between the two axes.
Parallel Axis Theorem Formula
Parallel axis theorem statement can be expressed as follows:
I = Ic + Mh2
Where,
I is the moment of inertia of the body
Ic is the moment of inertia about the center
M is the mass of the body
h2 is the square of the distance between the two axes
Parallel Axis Theorem Derivation
Let Ic be the moment of inertia of an axis that is passing through the centre of mass (AB from the figure) and I will be the moment of inertia about the axis A’B’ at a distance of h.
Consider a particle of mass m at a distance r from the centre of gravity of the body.
Then,
Distance from A’B’ = r + h
I = ∑m (r + h)2
I = ∑m (r2 + h2 + 2rh)
I = ∑mr2 + ∑mh2 + ∑2rh
I = Ic + h2∑m + 2h∑mr
I = Ic + Mh2 + 0
I = Ic + Mh2
Hence, the above is the formula of parallel axis theorem.