Home
Class 11
PHYSICS
Find the angular momentum of a disc abou...

Find the angular momentum of a disc about the axis shown in figure in the following situations.

Text Solution

Verified by Experts

Case a: In this case the disc is rotating about fixed axis which is parallel to the `z`-axis.
`Hence vecL=I_(z)(hatk)=((MR^(2))/2)omega(hatk)`
direction can be determined using right hand rule.
Case b: In this case also the disc rotates about fixed axis. We can write angular momentum for this situation.
`vecL=I_(z)omega(hatk)`
Uisnng parallel axis we can find the value of `I_(2)=(MR^(2))/2+Md^(2)` Hence `vecL=((MR^(2))/2+Md^(2))omega(hatk)`
Case c: In this case the disc is rotating about an axis parallel to the `z`-axis and centre of disc is also translating.
Hence, angular momentum,
`vecL=I_(cm)vecomega+vecrxxmvecv`
`=(MR^(2))/2omega(-hatk)+Mvd(-hatk)`
`=((MR^(2))/2omega+Mvd)(-hatk)`
Case d: In the case also the the disc is rotating about an axis passing through it centre and parallel to `y`-axis and centre of mass of disc is translating with velocity `v` parallel to `x`-axis
`vecL=I_(CM)omega(hatj)+Mvd(hatk)`
Here `I_(CM)=(MR^(2))/4`
Hence , `vecL=(MR^(2))/4omega(hatj)+Mvd(hatk)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • RIGID BODY DYNAMICS 2

    CENGAGE PHYSICS|Exercise Solved Examples|12 Videos

  • RIGID BODY DYNAMICS 2

    CENGAGE PHYSICS|Exercise Exercise 3.1|11 Videos

  • RIGID BODY DYNAMICS 1

    CENGAGE PHYSICS|Exercise Integer|11 Videos

  • SOUND WAVES AND DOPPLER EFFECT

    CENGAGE PHYSICS|Exercise Integer|16 Videos

Similar Questions

Explore conceptually related problems

A uniform rod of mass m and length L is fixed to an axis, making an angle theta with it as shown in the figure. The rod is rotated about this axis so that the free end of the rod moves with a uniform speed ‘v’. Find the angular momentum of the rod about the axis. Is the angular momentum of the rod about point A constant?

Find the angular momentum of the earth (a) about the sun due to its orbital motion and (b) about its axis due to its spinning motion.

Knowledge Check

  • A disc of mass M and radius R is rolling with angular speed omega on a horizontal plane. The magnitude of angular momentum of the disc about a point on ground along the line of motion of disc is :

    A
    `(1//2)MR^(2)omega`
    B
    `MR^(2)omega`
    C
    `(3//2)MR^(2)omega`
    D
    `2MR^(2)omega`

  • A disc of mass m and radius R moves in the x-y plane as shown in Fig. The angular momentum of the disc about the origin O at the instant shown is

    A
    `-5/2mR^(2)omegahatk`
    B
    `7/3mR^(2)omegahatk`
    C
    `-9/2mR^(2)omegahatk`
    D
    `5/2mR^(2)omegahatk`

  • The angular momentum of the atom will be constant about an axis passing through

    A
    nucleus
    B
    electron
    C
    centre of mass of the atom
    D
    any axis perpendicular to the line joining the electron and nucleus

    • Similar Questions

    Explore conceptually related problems

    In example number 12.16 suppose the disc starts rotating anticlockwise with the sae angular velocity omega=(v)/(R) , then what will e the angular momentum of te disc about bottommost in this new situation?

    A smooth horizontal disc rotates with a constant angular velocity omega about a stationary vertical axis passing through its centre, the point O. At a moment t=0 a disc is set in motion from that: point with velocity v_0 . Find the angular momentum M(t) of the disc relative to the point O in the reference frame fixed to the disc. Make sure that this angular momentum is caused by the Coriolis force.

    In the situation shown in figure, find the velocity of image.

    A disc of mass m and radius R is rolling on horizontal ground with linear velocity v. What is the angular momentum of the disc about an axis passing through bottommost point and perpendicular to the plane of motion ?

    The conservation of angular momentum, which corresponds to the conservation of linear momentum states that the angular momentum about an axis of a given rotating body of system of bodies is constant, if no external torque acts about that axis. The earth rotates about an axis passing through its geographic north and south poles with a period of one day. If its is struck by meteorites, then since action and reaction are equal, no external couple acts on the earth and metorites. Their total angular momentum is thus conserved. Neglecting the angular momentum of the meteorites about the earths axis before collision compared with that of the earth, then angular momentum of (earth + metorites) after collision = angular momentum of earth before collision. Since the effective mass of the earth has increassed after collision, the moment of inertia has increased. So the earth will slow down slightly. A uniform heavy disc is rotating at constant angular velocity about a vertical axis through its centre, some sand was dropped gently an the disc, the angular velocity of the disc.

    Home
    Profile