Tag: rotational motion of a rigid body and moment of inertia

Questions Related to rotational motion of a rigid body and moment of inertia

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

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. $100 rpm$

  2. $150 rpm$

  3. $200 rpm$

  4. $250 rpm$

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Correct Option: C

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)

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. $ 24 kg m^2s^{-1}$

  2. $24\sqrt{ 2} kg m^2s^{-1}$

  3. $12 kg m^2s^{-1}$

  4. $6\sqrt{ 2} kg m^2s^{-1}$

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Correct Option: C

 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 

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. About any point on the rod

  2. About a point at the centre of the rod

  3. About end point of the rod

  4. None

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Correct Option: C

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

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. $2 \sqrt {GM^3 r}$

  2. $\frac{1}{2} \sqrt {GM^3 r}$

  3. $\frac{1}{2} \sqrt {2GM^3 r}$

  4. $\frac{1}{2} \sqrt {\frac{GM^3 r}{2}}$

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Correct Option: D

Choose the INCORRECT statements

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. If Linear momentum of system is conserved then angular momentum of system must be also conserved.

  2. If angular momentum is conserved then angular velocity must be also conserved about the same axis.

  3. If not torque about any axis is zero then force must also be zero.

  4. If a rigid body is in translational equilibrium then its linear velocity is constant but angular velocity may be varying

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Correct Option: D

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.

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. I only

  2. III only

  3. I and II only

  4. II and III only

  5. I, II and III

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Correct Option: C

A circular ring of mass $1$ Kg and radius $0.2$ m executes $10$ revolutions per sec. Its angular momentum would be -$( kg-m^2/sec)$

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. $0.025$

  2. $0.25$

  3. $2.5$

  4. $25$

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Correct Option: B

The total angular momentum of a body is equal to the angular momentum  of its center of mass if the body has:

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. only rotational motion

  2. only translational motion

  3. both rotational and translational motion

  4. no motion at all

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Correct Option: C

 Two bodies of different masses have same K.E. The one having more momentum is

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. Heavier body

  2. lighter body

  3. both none

  4. both

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Correct Option: B
Explanation:

$K.E.$ for a given momentum is inversely proportional to the mass$.$

So$,$ the lighter mass has greater kinetic energy$.$ For two bodies having same kinetic energy$,$ the heavier one has greater momentum$.$
Hence,
option $(B)$ is correct answer.  

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:-

physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

  1. $1$

  2. $-1$

  3. $2$

  4. zero

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Correct Option: B
Explanation:

Given,
$\vec r=2\hat i-6\hat j-12\hat k$
$\vec F=\alpha\hat i +3\hat j+6\hat k$
For the conservation of angular momentum about origin, the torgue acting on the particle will be zero.
$\tau=\vec r\times \vec F$
$\vec r\times \vec F=0$
$(\alpha \hat i+3\hat j+6\hat k)\times (2\hat i-6\hat j-12\hat k)=0\hat i+0\hat j+0\hat k$
$\hat i(-36+36)-\hat j (12+12\alpha)+\hat k(6+6\hat k)=0\hat i+0\hat j+\hat k$
By equating it's coefficient, we get
$12+12\alpha =0$,   $6+6\alpha =0$
$12=-12\alpha$
$\alpha =-1$
The correct option is B.