Related Questions

When a body of mass moment of inertia '$$I$$' (about a given axis) is rotated about that axis with an angular velocity to, then the kinetic energy of rotation is
A hollow rod has frictionless inner walls. Inside the rod are two small spheres that are kept on either side of the centre of rod. The rod is rotated about its central axis which is perpendicular to the plane of rotation. If the rod had been rotated by an impulsive torque which gave it an instantaneous angular velocity of 5rad/s, what will be the angular velocity after some finite but long time ‘t’? Assume no external forces act on rod after the impulse. Also state what will happen to the spheres in the centre of the rod. The rod has a mass =2kg & length =10cm. The two spheres have a mass =1kg each.
The moment of inertia of a uniform sphere of radius, r about an axis passing through its centre is given by $$\frac{2}{5}\left( {\frac{{4\pi }}{3}{r^5}\rho } \right).$$    A rigid sphere of uniform mass density $$\rho $$ and radius R has two smaller spheres of radii $$\frac{R}{2}$$ hollowed out of it as shown in the figure given below.
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The moment of inertia of the resulting body about Y-axis is
A symmetrical body is rotating about its axis of symmetry, its moment of inertia about the axis of rotation being 1 kg-m2 and its rate of rotation 2 rev/sec. The angular momentum of the body in kg-m2/sec is
A disc is a spinning with an angular velocity $$\omega $$ rad/s about the axis of spin. The couple applied to the disc causing precession will be (where $$I$$ = Mass moment of inertia of the disc and $$\omega {\text{P}}$$  = Angular velocity of precession of the axis of spin)
According to parallel axis theorem, the moment of inertia of a section about an axis parallel to the axis through center of gravity (i.e. $${I_{\text{P}}}$$) is given by (where, A = Area of the section, $${I_{\text{G}}}$$ = Moment of inertia of the section about an axis passing through its C.G. and h = Distance between C.G. and the parallel axis.)
The moment of inertia of a body about a given axis is 1.2kgm2. Initially, the body at rest. In order to produce a rotational kinetic energy of 1500 joule, an angular acceleration of 25radian/sec2 must be applied about the axis for duration of ___________
Let I1 be the moment of inertia about the centre of mass of a thick asymmetrical body. Let I2 be the moment of inertia about an axis parallel to I1. The distance between the two axes is ‘a’ & the mass of the body is ‘m’. Find the relation between I1 & I2.
A rigid body is rotating about its centre of mass; fixed at origin with an angular velocity $$\overrightarrow \omega $$ and angular acceleration $$\overrightarrow \alpha $$. If the torque acting on it is $$\overrightarrow \tau $$ and its angular momentum is $$\overrightarrow {\bf{L}} $$, then the rate of change of its kinetic energy is
In order to have a connecting rod equally strong in buckling about X-axis and Y-axis, the moment of inertia about X-axis should be __________ the moment of inertia about Y-axis.