Rotational Motion

From a disc of radius $R$ and mass $M$, a circular hole of diameter $R$, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing…

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through

A small mass attached to a string rotates on frictionless table top as shown. If the tension is the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2 , the…

Match List-I with List-II List-I List-II (A) Moment of inertia of solid sphere of radius $R$ about any tangent. (I) $\frac{5}{3}\mathrm{MR}^{2}$ (B) Moment of inertia of hollow sphere of radius $\left(R\right)$ about…

A thin disc of mass $M$ and radius $R$ has mass per unit area $\sigma\,\left(r\right)=kr^{2}$ where $r$ is the distance from its centre. Its moment inertia about an axis going through its centre of mass and…

As shown in the figure, a bob of mass $m$ is tied to a massless string whose other end portion is wound on a fly wheel (disc) of radius $r$ and mass $m.$ When released from rest the bob starts falling vertically. When…

Let the moment of inertia of a hollow cylinder of length $30cm$ (inner radius $10cm$ and outer radius $20cm$), about its axis be $\text{I}$ . The radius of a thin cylinder of the same mass such that its moment of…

A rectangular solid box of length $0.3m$ is held horizontally, with one of its sides on the edge of a platform of height $5m$ . When released, it slips off the table in a very short time $\tau\,=0.01s$ , remaining…

A ball of mass $160g$ is thrown up at an angle of $60^{\circ}$to the horizontal at a speed of $10ms^{-1}$. The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the…

The linear mass density of a thin rod$\mathrm{AB}$of length$L$varies from$A$to$B$as$\lambda\,\left(x\right)=\lambda\,_{0}\left(1+\frac{x}{L}\right)$, where$x$is the distance from$A$. If$M$is the mass of the rod then its…

Moment of inertia of a cylinder of mass$m,$length $L$ and radius$R$ about an axis passing through its centre and perpendicular to the axis of the cylinder is$I=M\left(\frac{R^{2}}{4}+\frac{L^{2}}{12}\right).$ If such a…

A solid cylinder of mass $m$ is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is: [The…