What is the moment of inertia of uniform thin rod?

Figure 10.25 Calculation of the moment of inertia I for a uniform thin rod about an axis through the center of the rod. λ=mlorm=λl. λ = m l or m = λ l . I=∫r2dm=∫x2dm=∫x2λdx.

What is the moment of inertia of the rod if the axis of rotation is through its center?

If the axis of rotation passes through the center of the rod, then the moment of inertia is I=112mL2 I = 1 12 m L 2 .

What is the moment of inertia of the object about an axis through its center and perpendicular rod?

τ=r⋅F=mr2α. Note that it matters where we choose the rotation axis. For example, the moment of inertia of a rod of length L and mass m around an axis through its center perpendicular to the rod is 112mL2, whereas the moment of inertia around an axis perpendicular to the rod but located at one of its ends is 13mL2.

What is the moment of inertia of a thin rod of length l about its middle point?

The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is. Hence, net moment of inertia of complete structure through its middle point O is. =13[ML28+ML28]=ML212.

What is the moment of inertia of a sphere of radius r?

The moment of inertia of a sphere of mass M and radius R about an axis passing through its centre is 52​MR2.

What is uniform rod?

A uniform rod is a linear object with a constant linear density, and its center of gravity is at its midpoint. As we can see in the diagram above, a uniform rod would be perfectly balanced at its midpoint.

What is the symbol for moment of inertia?

symbol I
The Moment of Inertia is often given the symbol I. It is the rotational analogue of mass. In Newtonian physics the acceleration of a body is inversely proportional to mass.

What is the moment of inertia of a uniform circular disk of radius R?

The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is. =12MR2+MR2=32MR2.

What is the moment of inertia I of a uniform solid sphere of mass M and radius R?

Let us consider a sphere of radius R and mass M. A thin spherical shell of radius x, mass dm and thickness dx is taken as a mass element. Therefore, the moment of inertia of a uniform solid sphere (I) = 2MR2/5.