Angular momentum in case of rotation about a fixed axis - class-XI
| Description: angular momentum in case of rotation about a fixed axis | |
| Number of Questions: 84 | |
| Created by: Karuna Seth | |
| Tags: physics rigid body dynamics systems of particles and rotational motion option b: engineering physics motion of system of particles and rigid bodies rotational motion of a rigid body and moment of inertia |
A particle of mass m travels with a speed v along positive direction of x-axis parallel to the line y=4. At t=0, the particle is at (0,4),. The angular momentum of the particle about the origin is
A spinning ice skater can increase his rate of rotation by bringing is arms and free leg closer to his body.
How does this procedure affect the skater's angular momentum and kinetic energy?
The angular momentum of a moving body remains constant if
Which of the following laws is not always true as per the present world?
What should be the angular momentum of an electron in Bohr's hydrogen atom whose energy is -0.544 eV?
Angular momentum in $UCM$ is directed:
In absence of external forces on a rigid system, which of the following quantities must remain constant?
A particle of mass 2kg located at the position $\hat{i}+\hat{j}$ has a velocty$2(\hat{i}-\hat{j}+\hat{k})$ it s angular momentum about the x-axis in kg
Which parameters of all the particles of rotating fan are same :-
A man, sitting firmly over a rotating stool has his arms stretched. If he folds his arms, the work done by the man is :
A 40 Kg mass hanging at the end of a rope of length L oscillates in a vertical plane with an angular amplitude $ \theta _o $. If the breaking strength of the rope is 80 Kg. Wt What is the maximum angular amplitude so that the mass can oscillates without the rope breaking ?
Angular momentum of an electron having energy -0.85 eV in hydrogen atom, will be
Assertion (A): Even though a planet revolve around the sun in an elliptical orbit, the angular momentum of planet is constant.
Reason (R) : Any force other than mutual gravitational force is absent between the planet and the sun.
The law of conservation of angular momentum is obtained from Newton's II law in rotational motion when:
The energy of electron in an excited hydrogen atom is -3.4 eV. Its angular momentum according to Bohr's theory will be:
Under the action of a central force, there is a conservation of-
Four particles of masses in the ratio 1:2:3:4 are rotating in concentric circles of radii proportional to their masses with the same angular velocity. What is the angular momentum of the system
Two identical particles of mass m move in a circle of radius r , 180 degrees out of phase at an angular speed $\omega$ about the z-axis in a plane parallel to but a distance h above the x-y plane (Figure 19.14). Find the magnitude and the direction of the angular momentum L relative to the origin.
Two identical particles of mass m are separated by a distance of 1 metre each and are rotating with a constant speed of 5 m/s . What will be their angular momentum about an axis distant 0.8 m from the first particle on the line joining them
A particle is in uniform circular motion in a horizontal plane. Its angular momentum is constant when the origin is taken at
A particle starts from the point 0.8 m and moves with a uniform velocity of 3 m/s. what is the angular momentum of the particle after 5 seconds about origin.mass of the particle is 1 kg.
The instantaneous angular position of a point on a rotating wheel is given by the equation $\theta(t)=2t^{3}-6t^{2}$. The torque on the wheel becomes zero at :
Let $A$ be the area swept by the line joining the earth and the sun during Feb 2012. The area swept by the same line during the first week of that month is
(i) Linear momentum is proportional to $1/n$
(ii) Radius is proportional to $n$
(iii) Kinetic energy is proportional to $1/n^{2}$
(iv) Angular momentum is proportional to $n$
Choose the correct option from the codes given below.
The position of a particle is given by $\overrightarrow { r } =(\hat{i} +2\hat{j} -\hat{k})$ and momentum $\overrightarrow { P } =(3\hat{i} +4\hat{j} -2\hat{k})$. The angular momentum is perpendicular to
A particle of mass $1\ kg$ is projected at an angle $ \theta $ with horizontal. Its co-ordinates at any instant are $(5m,5m)$ and itis having velocity components along $X- $axis and $Y-$axis as $8\ m/s$ and $4\ m/s$ respectively. Its angular momentum about the origin is
A particle of mass m = 5 units is moving with a uniform speed v = $3\sqrt2$ units in the XY - plane along the line y = x + 4.The magnitude of the angular momentum about origin is
The angular momentum of an electron in a hydrogen atom is proprotional to ( where r is redius of orbit)
If a particle of mass m is moving with constant velocity V parallel to X-axis along $y=axis$. The angular momentum with respect to origin at any time 't' is
The rotational kinetic energy of a hollow spherical shell 2.5 J. If its frequency of rotation is made 10 times, then new kinetic energy will be -
The angular momentum of an electron revolving in a circular orbit is J, What is its magnetic moment?
$E _n$ and $J _n$ denote the total energy magnitude and the angular momentum of an electron in the nth allowed orbit of the Both atom .Then:
A wooden block of mass $2\ m$ is hung with the help of a light string of length $l$ in the vertical plane.
A bullet of mass $\dfrac{m}{4}$ moving horizontally with velocity $v _{0}\left(v _{0}=\sqrt{5gl}\right)$ penetrates the block and comes out with velocity $\dfrac{v _{0}}{2}$. The maximum height reached by the block is (Assume string remains vertical till bulled passes through the block)
A person standing on a rotating platform has his hands lowered. He suddenly outstretch his arms. The angular momentum.
If a person sitting on a rotating stool with his hands outstretched, suddenly lowers his hands, then his :
A man spinning in free space changes the shape of his body, eg. by spreading his arms or curling up. By doing this, he can change his :
Two particles are initially moving with angular momentum $\vec{L _{1}}$ and $\vec{L _{2}}$ in a region of space with no external torque. A constant external torque $\vec{\tau}$ then acts on one particle, but not on the other particle, for a time interval $\Delta{t}$. What is the change in the total angular momentum of the two particles?
uniform disc of mass M and radius R is rotating about its centre of mass (the centre of mass is at rest )with an angular speed $\omega $.the angular momentum of disc about a point A (as shown)will be.
when a mass is rotating in a plane about a fixed point, its angular momentum is directed along
The angular momentum of a system of particles is conserved
A ballet dancer spins about a vertical axis at $120 rpm$ with arms stretched with her arms folded the moment of inertia about the axis of rotation decreases by $40\%$ calculate new rate of rotation
A particle of mass $300 g$ is moving with a speed of $20 ms-1$ along the straight line $y= x-4\sqrt { 2 }$. The angular momentum of the particle about the origin is (where y & x are in metres)
A rod of mass M and length L is placed on a smooth horizontal table and is hit by a ball moving horizontally and perpendicular to length of rod and sticks to it.Then conservation of angular momentum can be applied
Two spherical bodies of equal mass (M) revolve about their centre of mass. The distance between the centre of the two masses is r. The angular momentum of each about their centre of mass is
Choose the INCORRECT statements
A satellite with a mass of $M$ moves in a circular orbit of radius $R$ at a constant speed of $v$. Which of the following must be true?
(I) The net force on the satellite is equal to MR and is directed toward the centre of the orbit,
(II) The net work done on the satellite by gravity in one revolution is zero.
(III) The angular momentum of the satellite is constant.
A circular ring of mass $1$ Kg and radius $0.2$ m executes $10$ revolutions per sec. Its angular momentum would be -$( kg-m^2/sec)$
The total angular momentum of a body is equal to the angular momentum of its center of mass if the body has:
Two bodies of different masses have same K.E. The one having more momentum is
A force $\vec F = \alpha \hat i + 3\hat j + 6\hat k$ is acting at a point $\vec r = 2\hat i - 6\hat j - 12\hat k$. The value of $\alpha$ for which angular momentum about the origin is conserved is:-
A unit mass at position vector $\vec { r } = ( 3 \hat { i } + 4 \hat { j } )$ is moving with a velocity $\vec { v } = ( 5 \hat { i } - 6 \hat { j } )$ What is the angular momentum of the body about the origin
A man standing on a platform holds weights in his outstretched arms. The system rotates freely about a central vertical axis. If he now draws the weights inwards close to his body,
A particle performs uniform circular motion with an angular momentum L. If the frequency of particle's motion is doubled and its kinetic energy halved, the angular momentum becomes:
What is the magnitude of vertical force required to produced a moment of 20 Nm at point A (1 m, 1 m) if the force is acting at point B (2m,2m)
A stone tied to one end of the string is revolved round a rod in such a way that the string winds over the rod and get shortened. In this process which of the following quantities remain constant?
A swimmer while jumping into water from a height easily forms a loop in air, if
If no external force acts on a system
Two loops P and Q are made from a uniform wire. The radii of P and Q are $r _1$ and $r _2$ respectively, and their moments of inertia about their own axises are $I _1$ and $I _2$ respectively. If $I _2 = 4I _1$, the $r _1/r _2$ equals:
A particle moves on a circular path with decreasing speed. Choose the correct statement.
A particle of mass 2 kg located at the position $ \left( \hat { i } +\hat { j } \right) m $ has a velocity $ 2\left( \hat { i } -\hat { j } +\hat{ k } \right) ms^{-1} $ . Its angular momentum along z-axis in $ kgm^2 s^{-1} $ is
Angular momentum of a system a particles changes, when
A gymnast takes turns with her arms & legs stretched. When she pulls her arms & legs in
If a running boy jumps on a rotating table, which of the following is conserved?
In which of the following case(s), the angular momentum is conserved ?
When tall buildings are constructed on earth, the duration of day night
If the ice at the poles melts and flows towards the equator, how will it affect the duration of day-night?
A cylinder is rolling down a rough inclined plane. Its angular momentum about the point of contact remains constant. Is this statement true or false?
A uniform thin circular ring of mass 'M' and radius 'R' is rotating about its fixed axis, passing through its centre and perpendicular to its plane of rotation, with a constant angular velocity $\omega$. Two objects each of mass m, are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity of :
A student is rotating on a stool at an angular velocity $'\omega'$ with their arms outstretched while holding a pair of masses. The frictional effects of the stool are negligible.
Which of the following actions would result in a change in angular momentum for the student?
A solid cylinder of mass, $m$, and radius, $r$, is rotating at an angular velocity, $\omega$ when a non-rotating hoop of equal mass and radius drops onto the cylinder.
In terms of its initial angular velocity, $\omega$, what is its new angular velocity, ${\omega}^{\prime}$?
A bar of length l carrying a small mass m at one of its ends rotates with a uniform angular speed $\omega$ in a vertical plane about the mid-point of the bar. During the rotation, at some instant of time when the bar is horizontal, the mass is detached from the bar but the bar continues to rotate with same $\omega$. The mass moves vertically up, comes back and reches the bar at the same point. At that place, the acceleration due to gravity is g.
A body is moving on a rough horizontal plate in a circular path being tide to a nail (at the centre) by a string, while the body is in motion the friction force of the body
A dancer is rotating on smooth horizontal floor with an angular momentum $L$. The dancer folds her hands so that her momentof inertia decreases by $25$%. The new angular momentum is.
Two men of equal masses stand at opposite ends of the diameter of a turntable disc of a certain mass, moving with constant angular velocity. The two men make their way to the middle of the turntable at equal rates. In doing so will
A circular disk of moment of inertia $I _t$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $\omega _i$. Another disk of moment of inertia $I _b$ is dropped co-axially onto the rotating disk.Initially the second disk has zero angular speed.Eventually both the disks rotate with a constant angular speed $\omega _p$ .The energy lost by the initially rotating disc due to friction is
Two particles each of mass m move in opposite direction along Y-axis. One particle moves in positive direction with velocity v while the other particle moves in negative direction with speed 2v. The total angular momentum of the system with respect to origin is:
The shape of the orbit a planet depends on:
A man standing on a platform holds weight in his outstreached arms. The system rotates freely about a central vertical axis. If he now draws the weights inward close to his body
A force $\vec { F } =\alpha \hat { i } +3\hat { j } +6\hat { k }$ is acting at a point $\vec { r } =2\hat { i } -6\hat { j } -12\hat { k }$. The value of $\alpha$ for which angular momentum about origine is conserved is
A point sized sphere of mass $'m'$ is suspended from a point using a string of length $'l'$. It is pulled to a side till the string is horizontal and released. As the mass passes through the portion where the string is vertical, magnitude of its angular momentum is:
A disc of mass $100\ g$ and radius $10\ cm$ has a projection on its circumference. The mass of projection is negligible. A $20\ g$ bit of putty moving tangential to the disc with a velocity of $5\ m\ s^{-1}$ strikes the projection and sticks to it. The angular velocity of disc is
A stationary body explodes into two fragments of masses ${m} _{1}$ and ${m} _{2}$. If momentum of one fragment is $p$, the minimum energy of explosion is
A particle of mass $5kg$ is moving with a uniform speed $3\sqrt{2}$ in $XOY$ plane along the line $Y=X+4$. The magnitude of its angular momentum about the origin is:
A circular platform is mounted on a vertical frictionless axle. Its radius is $r=2m$ and its moment inertia is $I=200kg$ ${m}^{2}$. It is initially at rest. A $70kg$ man stands on the edge of the platform and begins to walk along the edge at speed ${v} _{0}=10{ms}^{-1}$ relative to the ground. The angular velocity of the platform is