Rotational Motion

A solid metallic sphere of radius ' $R$ ' having moment of inertia '$I$' about diameter is melted and recast into a solid disc of radius ' $r$ ' of a uniform thickness. The moment of inertia of a disc about an axis passing through its edge ...

A ring and a disc roll on horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is 6 J then total kinetic energy of the disc is

Two bodies A and B have their moments of inertia $I_1$ and $I_2$ respectively about their axis of rotation. If their kinetic energies of rotation are equal and their angular momenta $\mathrm{L}_1$ and $\mathrm{L}_2$ respectively are in the ...

Two discs of same mass and same thickness (t) are made from two different materials of densities '\(d_1\)' and '\(d_2\)' respectively. The ratio of the moment of inertia \(I_1\) to \(I_2\) of two discs about an axis passing through the cent...

A solid sphere rolls without slipping on an inclined plane at an angle \(\theta\). The ratio of total kinetic energy to its rotational kinetic energy is

A square lamina of side '\(b\)' has same mass as a disc of radius '\(R\)' the moment of inertia of the two objects about an axis perpendicular to the plane and passing through the centre is equal. The ratio \(\frac{b}{R}\) is

A disc of radius \(R\) and thickness \(\frac{R}{6}\) has moment of inertia I about an axis passing through its centre and perpendicular to its plane. Dise is melted and recast into a solid sphere. The moment of inertia of a sphere about its...

A thin uniform rod of mass '\(m\)' and length '\(P\)' is suspended from one end which can oscillate in a vertical plane about the point of intersection. It is pulled to one side and then released. It passes through the equilibrium position ...

A mass '\(M\)' is moving with constant velocity parallel to \(\mathrm{X}\)-axis. Its angular momentum with respect to the origin is

A solid cylinder and a solid sphere having same mass and same radius roll down on the same inclined plane. The ratio of the acceleration of the cylinder '\(a_c\)' to that of sphere '\(a_s\)' is

Four identical uniform solid spheres each of same mass '\(M\)' and radius '\(R\)' are placed touching each other as shown in figure, with centres A, B, C, D. \(\mathrm{I}_{\mathrm{A}}, \mathrm{I}_{\mathrm{B}}, \mathrm{I}_{\mathrm{C}}\) and ...

A solid cylinder of mass \(3 \mathrm{~kg}\) is rolling on a horizontal surface with velocity \(4 \mathrm{~m} / \mathrm{s}\). It collides with a horizontal spring whose one end is fixed to rigid support. The force constant of material of spr...

The rotational kinetic energy and translational kinetic energy of a rolling body are same, the body is

A rigid body rotates with an angular momentum L. If its rotational kinetic energy is made four times, its angular momentum will become

A thin uniform \(\operatorname{rod} A B\) of mass \(m\) and length \(l\) is hinged at one end \(A\) to the ground level. Initially the rod stands vertically and is allowed to fall freely to the ground in the vertical plane. The angular velo...

Four identical uniform solid spheres each of same mass \(M\) and radius \(R\) are placed touching each other as shown in figure with centres \(A, B, C, D. I_A, I_B, I_C, I_D\) are the moment of inertia of these spheres respectively about an...

A thin uniform circular disc of mass '\(\mathrm{M}\)' and radius '\(R\)' is rotating with angular velocity '\(\omega\)', in a horizontal plane about an axis passing through its centre and perpendicular to its plane. Another disc of same rad...

\(I_1\) is the moment of inertia of a circular disc about an axis passing through its centre and perpendicular to the plane of disc. \(I_2\) is its moment of inertia about an axis \(A B\) perpendicular to plane and parallel to axis $$\mathr...

In \(\mathrm{P}^{\text {th }}\) second, a particle describes angular displacement of '\(\beta\)' rad. If it starts from rest, the angular acceleration is

A thin wire of length '\(L\)' and uniform linear mass density '\(m\)' is bent into a circular coil. The moment of inertia of this coil about tangential axis and in plane of the coil is

A disc has mass \(M\) and radius \(R\). How much tangential force should be applied to the rim of the disc, so as to rotate with angular velocity '\(\omega\)' in time \(\mathrm{t}\) ?

Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its plane is \(\mathrm{K}_{\mathrm{c}}\). Radius of gyration of the same disc about a diameter of the disc is \(K_d\). The rat...

A particle moves along a circular path with decreasing speed. Hence

From a disc of mass '\(M\)' and radius '\(R\)', a circular hole of diameter '\(R\)' is cut whose rim passes through the centre. The moment of inertia of the remaining part of the disc about perpendicular axis passing through the centre is

Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio

A particle of mass '\(\mathrm{m}\)' is rotating along a circular path of radius '\(r\)' having angular momentum '\(L\)'. The centripetal force acting on the particle is given by

Seven identical discs each of mass \(M\) and radius \(\mathrm{R}\) are arranged in a hexagonal plane pattern so as to touch each neighbour disc as shown in the figure. The moment of inertia of the system of seven discs about an axis passing...

If 'I' is moment of inertia of a thin circular disc about an axis passing through the tangent of the disc and in the plane of disc. The moment of inertia of same circular disc about an axis perpendicular to plane and passing through its cen...

The moment of inertia of a uniform square plate about an axis perpendicular to its plane and passing through the centre is \(\frac{\mathrm{Ma}^2}{6}\), where '\(M\)' is the mass and '\(a\)' is the side of square plate. Moment of inertia of ...

Two spheres each of mass '\(M\)' and radius \(\frac{R}{2}\) are connected at the ends of massless rod of length '\(2 R\)'. What will be the moment of inertia of the system about an axis passing through centre of one of the spheres and perpe...

What is the moment of inertia of the electron moving in second Bohr orbit of hydrogen atom? [ \(\mathrm{h}=\) Planck's constant, \(\mathrm{m}=\) mass of electron, \(\varepsilon_0=\) permittivity of free space, \(\mathrm{e}=\) charge on elec...

A body of mass '\(\mathrm{m}\)' and radius of gyration '\(\mathrm{K}\)' has an angular momentum \(\mathrm{L}\). Its angular velocity is

Two identical particles each of mass '\(m\)' are separated by a distance '\(d\)'. The axis of rotation passes through the midpoint of '\(\mathrm{d}\)' and is perpendicular to the length \(\mathrm{d}\). If '\(\mathrm{K}\)' is the average rot...

The moment of inertia of a thin uniform rod of mass 'M' and length 'L' about an axis passing through a point at a distance \(\frac{L}{4}\) from one of its ends and perpendicular to the length of the rod is

Three solid spheres each of mass '\(M\)' and radius '\(R\)' are arranged as shown in the figure. The moment of inertia of the system about YY' will be

Figure shows triangular lamina which can rotate about different axes moment of inertia is maximum, about the axis

A molecule consists of two atoms each of mass '\(m\)' and separated by a distance '\(\mathrm{d}\)'. At room temperature, if the average rotational kinetic energy is '\(E\)' then the angular frequency is

A metre scale is supported on a wedge at its centre of gravity. A body of weight 'w'. is suspended from the \(20 \mathrm{~cm}\) mark and another weight of 25 gram is suspended from \(74 \mathrm{~cm}\) mark balance it and the metre scale rem...

A body of mass 'm' and radius of gyration 'K' has an angular momentum 'L'. Then its angular velocity is

The moment of inertia of a body about the given axis, rotating with angular velocity 1 rad/s is numerically equal to 'P' times its rotational kinetic energy. The value of 'P' is

Two circular loops P and Q are made from a uniform wire. The radii of P and Q are R\(_1\) and R\(_2\) respectively. The momentsw of inertia about their own axis are \(\mathrm{I_P}\) and \(\mathrm{I_Q}\) respectively. If $$
\frac{\mathrm{I}_...

A solid sphere of mass '\(M\)' and radius '\(R\)' is rotating about its diameter. A solid cylinder of same mass and same radius is also rotating about its geometrical axis with an angular speet twice that of the sphere. The ratio of the kin...

Two rotating bodies \(P\) and \(Q\) of masses '\(\mathrm{m}\)' and '\(2 \mathrm{~m}\)' with moment of inertia \(I_P\) and \(I_Q\left(I_Q > I_P\right)\) have equal Kinetic energy of rotation. If \(\mathrm{L}_P\) and \(\mathrm{L}_Q\) be their...

Two rings of radius 'R' and 'nR' made of same material have the ratio of moment of inertia about an axis passing through its centre and perpendicular to the plane is \(1: 8\). The value of '\(n\)' is (mass per unit length \(=\lambda\))

A child is standing with folded hands at the centre of the platform rotating about its central axis. The kinetic energy of the system is '\(K\)'. The child now stretches his arms so that the moment of inertia of the system becomes double. T...

A particle with position vector \(\overrightarrow{\mathrm{r}}\) has a linear momentum \(\overrightarrow{\mathrm{P}}\). Which one of the following statements is true in respect of its angular momentum 'L' about the origin?

The moment of inertia of a body about a given axis is \(1.2 \mathrm{~kg} / \mathrm{m}^3\). Initially the body is at rest. In order to produce rotational kinetic energy of \(1500 \mathrm{~J}\), an angular acceleration of $$25 \mathrm{rad} / ...

The moment of inertia of a circular disc of radius \(2 \mathrm{~m}\) and mass \(1 \mathrm{~kg}\) about an axis XY passing through its centre of mass and perpendicular to the plane of the disc is \(2 \mathrm{~kg} \mathrm{~m}^2\). The moment ...

Three rings each of mass 'M' and radius 'R' are arranged as shown in the figure. The moment of inertia of system about axis YY' will be

A particle performs rotational motion with an angular momentum 'L'. If frequency of rotation is doubled and its kinetic energy becomes one fourth, the angular momentum becomes.