Rotational Motion

A solid sphere $A$ of radius $R$ and mass $M$ is attached at a point to a smaller solid sphere $B$ of radius $r

A thin horizontal disc is rotating about a vertical axis passing through its fixed centre $O$. Its angular momentum is $L_A$ and $L_B$ computed about points $A$ and $B$, respectively, with $O B=2 \times O A$. The value of $\frac{L_A}{L_B}$ ...

A thin wire of length ' $L$ ' and linear mass density ' $m$ ' is bent into a circular ring (in $x-y$ plane) with centre ' $C$ ' as shown in figure. The moment of inertia of the ring about an axis $y y^{\prime}$ will be:

The angular speed of a flywheel is increased from 600 rpm to 1200 rpm in 10 s . The number of revolutions completed by the flywheel during this time is:

A sphere of radius $R$ is cut from a larger solid sphere of radius $2 R$ as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the $Y$-axis is:

A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall making an angle of $60^{\circ}$ with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (Take $g=10 \ma...

The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence? Assume the Sun to be a sphere of uniform density.

The radius of gyration of a solid sphere of mass \(5 \mathrm{~kg}\) about \(X Y\) is \(5 \mathrm{~m}\) as shown in figure. The radius of the sphere is \(\frac{5 x}{\sqrt{7}} \mathrm{~m}\), then the value of $x$ is:

A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is \(v\) in the direction shown, which one of the following options is correct (\(P\) and \(Q\) are any highest and lowest points on the ...

A bob is whirled in a horizontal plane by means of a string with an initial speed of \(\omega \mathrm{~rpm}\). The tension in the string is \(T\). If speed becomes \(2 \omega\) while keeping the same radius, the tension in the string become...

The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is \(2400 \mathrm{~g} \mathrm{~cm}^2\). The length of the \(400 \mathrm{~g}\) rod is nearly:

A constant torque of \(100 \mathrm{~N} \mathrm{~m}\) turns a wheel of moment of inertia \(300 \mathrm{~kg} \mathrm{~m}^2\) about an axis passing through its centre. Starting from rest, its angular velocity after \(3 \mathrm{~s}\) is :-

The angular acceleration of a body, moving along the circumference of a circle, is :

The ratio of radius of gyration of a solid sphere of mass \(M\) and radius \(R\) about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :-

An energy of 484 J is spent in increasing the speed of a flywheel from 60 rpm to 360 rpm. The moment of inertia of the flywheel is :

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is

The angular speed of a fly wheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration in rad/s2 is

A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass 'm' is suspended from the rod at 160 cm mark as shown in the figure. Find ...

From a circular ring of mass 'M' and radius 'R' an arc corresponding to a 90\(^\circ\) sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the center of the ring and perpendicular to the ...

Find the torque about the origin when a force of 3 \(\hat j\)
N acts on a particle whose position vector is 2 \(\hat k\) m.

Two particles A and B are moving in uniform circular motion in concentric circles of radii rA and rB with speed vA and vB respecitively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be :

A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2\(\pi\) revolutions is :

A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it?

A solid sphere is rotating freely about its
symmetry axis in free space. The radius of
the sphere is increased keeping its mass same.
Which of the following physical quantities
would remain constant for the sphere?

The moment of the force, \(\overrightarrow F = 4\widehat i + 5\widehat j - 6\widehat k\) at
(2, 0, –3), about the point (2, –2, –2), is given by

Three objects, A : (a solid sphere), B : (a thin
circular disk) and C : (a circular ring), each
have the same mass M and radius R. They
all spin with the same angular speed \(\omega\) about
their own symmetry axes. The amounts of
work (W) ...

A solid sphere is in rolling motion. In rolling
motion a body possesses translational kinetic
energy (Kt) as well as rotational kinetic energy
(Kr) simultaneously. The ratio Kt
: (Kt + Kr)
for the sphere is

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities \({\omega _1}\) and \({\omega _2}\). They are brought into contact face to face coi...

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?

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 speed twice that of the sphere. The ratio of their kinetic energ...

A light rod of length \(l\) has two masses m1 and m2 attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is

Two rotating bodies A and B of masses m and 2m with moments of inertia \({I_A}\) and \({I_B}\) (\({I_B}\) > \({I_A}\)) have equal kinetic energy of rotation. If LA and LB be their angular momenta respectively, then

A disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

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 through the centre?

A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of 2.0 rad s\(-\)2. ...

Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX' which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of th...

A mass m moves in a circle on a smooth horizontal plane with velocity v0 at a radius R0. The mass is attached to a string which passes through a smooth hole in the plane as shown. the tension in the string is increased gradually and finally...

A rod of weight W is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knives are at a distance d from each other. The centre of mass of the rod is at distance x from A. The normal reaction ...

An automobile moves on a road with a speed of 54 km h\(-\)1. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m2. If the vehicle is brought to rest in 15 s, the magnitude of averag...

Point masses m1 and m2 are placed at the opposite ends of a rigid rod of length L, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass ...

A force \(\overrightarrow F = \alpha \widehat i + 3\widehat j + 6\widehat k\) is acting at a point \(\overrightarrow r = 2\widehat i - 6\widehat j - 12\widehat k\). The value of \(\alpha\) for which angular momentum about origin is conse...

A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an an...

The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle \(\theta\) without slipping and slipping down the incline without rolling is

The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centres and perpendicular to their planes are

Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D1 has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s\(-\)1. Disc D2 has 4 kg mass, 0.1 m radius and initia...

A small object of uniform density rolls up a curved surface with an initial velocity 'v'. It reaches upto a maximum height of \({{3{v^2}} \over {4g}}\) with respect to the initial position. The object is

A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is

A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45o, the speed of the car is

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

ABC is an equilateral triangle with O as its centre. \({\overrightarrow F _1},{\overrightarrow F _2}\) and \({\overrightarrow F _3}\) represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is z...