Tag: angular momentum (l) and conservation of angular momentum

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Questions Related to angular momentum (l) and conservation of angular momentum

Multiple choice 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

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

  1. $100 rpm$

  2. $150 rpm$

  3. $200 rpm$

  4. $250 rpm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By conservation of angular momentum, I1 * w1 = I2 * w2. Given I2 = 0.6 * I1 and w1 = 120 rpm, we have 120 * I1 = w2 * 0.6 * I1, which simplifies to w2 = 120 / 0.6 = 200 rpm.

Multiple choice 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

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)

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

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

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

  4. $6\sqrt{ 2} kg m^2s^{-1}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice 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

 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 

  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
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When a ball strikes a rod on a smooth table, there is an impulsive reaction force at the point of contact. Angular momentum is conserved about any point where the net external torque is zero; for the end point, the impulsive reaction force at the pivot (if it were fixed) or the specific geometry makes the calculation valid.

Multiple choice 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

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

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

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

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

  4. $\frac{1}{2} \sqrt {\frac{GM^3 r}{2}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For two masses M revolving about their center of mass at distance r/2, the orbital velocity v is found from GM^2 / r^2 = M * v^2 / (r/2). Thus v^2 = GM / 2, so v = sqrt(GM / 2). Angular momentum L = M * v * (r/2) = M * sqrt(GM / 2) * (r/2) = (1/2) * sqrt(GM^3 * r^2 / 2) = (1/2) * sqrt(GM^3 * r / 2).

Multiple choice 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

Choose the INCORRECT statements

  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
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If a rigid body is in translational equilibrium, the net force is zero, but the angular velocity can be constant or changing depending on the net torque. The statement that angular velocity must be constant is incorrect.

Multiple choice 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

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.

  1. I only

  2. III only

  3. I and II only

  4. II and III only

  5. I, II and III
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice 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

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

  1. only rotational motion

  2. only translational motion

  3. both rotational and translational motion

  4. no motion at all
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice 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

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

  1. Heavier body

  2. lighter body

  3. both none

  4. both
Reveal answer Fill a bubble to check yourself
B Correct answer
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.  

Multiple choice 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

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:-

  1. $1$

  2. $-1$

  3. $2$

  4. zero
Reveal answer Fill a bubble to check yourself
B Correct answer
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.