Physics System of Particles and Rotational Motion

A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rads^-1 in a horizontal plane about an axis vertical to its plane and passing through the centre of the ring. If two objects each of mass m be attached gently to the opposite ends of a diameter of ring, the will then rotate with an angular velocity (in rads^-1).

The momentum of inertia of a uniform thin rod about a perpendicular axis passing through on end is I₁. The same rod is into a ring and its moment of inertia about a diameter is I₂. If $\frac{I_1}{I_2}is\frac{X{\pi }^2}{3},$  then the value of x will be__________.

A wheel is rotating at 900 r.p.m. about its axis. When power is cut of fit comes to rest in 1 minute. The angular retardation in rad/s² is

A square of mass m is made of thin wire with sides of length a. Calculate the rotational inertia about the z-axis.

The position vector of 1kg object is $\overrightarrow{r}=\left(3\widehat{i}-\widehat{j}\right)m$ and its velocity $\overrightarrow{v}=\left(3\widehat{j}+\widehat{k}\right)m{s}^{-1}.$ The magnitude of is angular momentum is $\sqrt[]{x}Nm$  where x is________.

Three points masses $m,2m$ and 3m are located at the vertices of an equilateral triangle of side ' a '. The moment of inertia of the system about an axis along the altitude of the triangle passing through m is $\frac{N}{20}m{a}^2$ where N is an integer. The value of N is

The torque $\stackrel{?}{\tau }$ acts on a body about a given point is found to be equal to $\stackrel{?}{A}*\stackrel{?}{L}$ where $\stackrel{?}{A}$ is a constant nonzero vector and $\stackrel{?}{L}$ is the angular momentum of the body about that point. Choose the incorrect option: $(\stackrel{?}{A}\ne \pm \hat{L})$

Three rods of equal mass having length L, L and √2L are joined to form a triangular frame as shown in the figure. The system is rotating about an axis passing through the vertex of the triangle and perpendicular to the plane of the triangle with an angular velocity ω. Find the angular momentum of the system.

Three thin rods of mass m and length a each are joined to form a triangle ABC in vertical plane. The triangle is pivoted at the vertex A such that it can rotate in the vertical plane. It is released from rest when the side AB is horizontal as shown. As the triangle rotates, the maximum velocity of the vertex B, VMAX , is given by:

Moment of inertia (M.I) of four bodies, having same mass and radius, and reported as:

I₁ = M.I. of thin circular ring about its diameter

I₂ = M.I. of circular disc about an axis perpendicular to disc and going through the centre,

I₃ = M.I. of solid cylinder about its axis and

I₄ = M.I. of solid sphere about its diameter.