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 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 

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

  2. 4 mv directed along the positive z- axis

  3. 4 mv directed along the negative z- axis

  4. 4 mv directed along the positive y- axis

Show answer
Correct Option: C
Explanation:
The correct option is C

We have,

$Mass=m,Speed=v$

A particle is moving along a straight line parallel to the y-axis.

So, position vector $(\hat r ) = 4 \hat j$ 

velocity of body $\hat V = v \hat i$

Since we know,

Angular momentum = $m(\hat r \times\hat V)$

$=m ( 4 \hat j \times v \hat i)$

$=-4mv\hat k$

Since,

$I \times j = k$ 
And, $j \times i = - k$

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?

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. Angular momentum remains the same while kinetic energy increases

  2. Angular momentum remains the same while kinetic energy decreases

  3. Both angular momentum and kinetic energy remain the same

  4. Angular momentum increases while kinetic energy remains the same

Show answer
Correct Option: C

The angular momentum of a moving body remains constant if

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. net external force is applied

  2. net pressure is applied

  3. net external torque is applied

  4. net external torque is not appled

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Correct Option: D

Which of the following laws is not always true as per the present world?

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. Law of conservation of Angular momentum

  2. Law of conservation of Charge 

  3. Law of conservation of linear momentum

  4. Law of conservation of Energy 

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Correct Option: C

What should be the angular momentum of an electron in Bohr's hydrogen atom whose energy is -0.544 eV?

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. $\large \frac{h}{\pi}$

  2. $\large \frac{3h}{2\pi}$

  3. $\large \frac{5h}{2\pi}$

  4. $\dfrac{2h}{2\pi}$

Show answer
Correct Option: C

Angular momentum in $UCM$ is directed:

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. Perpendicular to the plane of $UCM$

  2. Angular radius and away from centre

  3. Along radius and toward the centre

  4. Tangential to the $UCM$

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Correct Option: C

In absence of external forces on a rigid system, which of the following quantities must remain 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. angular momentum

  2. linear momentum

  3. moment of inertia

  4. kinetic energy

Show answer
Correct Option: A,B

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 

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. Zero

  2. 8

  3. 12

  4. 4

Show answer
Correct Option: B

Which parameters of all the particles of rotating fan are same :-

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 angular $( \theta, \omega, \alpha)$

  2. Only linear (s,v,a)

  3. Both linear and angular

  4. None of them

Show answer
Correct Option: A
Explanation:

In a rotational motion, only the angular parameters ($\theta, w,\alpha$) are same but not the linear parameters.

A man, sitting firmly over a rotating stool has his arms stretched. If he folds his arms, the work done by the man 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. zero

  2. positive

  3. negative

  4. may be positive or negative

Show answer
Correct Option: B
Explanation:

When the arms are stretched the rotational inertia is higher. When the man folds his arm he is basically decreasing his rotational inertia thereby gaining more angular velocity using the principle of conservation of angular momentum. This implies more angular distance is covered in the same time giving us positive work.