Tag: law of conservation of angular momentum

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Questions Related to law of 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 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.

  1. $12kgm^2$/s

  2. $24 kgm^2/s$

  3. $32 kgm^2/s$

  4. $44 kgm^2/s$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The correct option is B

Given,

$mass=1kg$

$t=5s$

$velocity=3m/s$

The angular momentum of the particle about a fixed position is given by:

$L = r \times mV$

So it is the product of momentum of a particle and its perpendicular distance from the fixed position.


Here particle is moving along the x-direction



So its momentum is along the x-direction

$P = mv = 1\times3 = 3 kgm/s$

Now, the perpendicular distance from origin to the momentum of particle is:

$r = 8 m$

Now, angular momentum is


$L = 8\times3 = 24 kg m^2/s$

So angular momentum is $ 24 kg m^2/s$
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 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 :

  1. $t=1s$

  2. $t=0.5\ s$

  3. $t=0.25\ s$

  4. $t=2s$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given, $\theta (t)=2t^3-6t^2$

We, know $T=\propto \dfrac{Id^2 \theta}{dt^2}=I\dfrac{d}{dt}(\dfrac{d \theta}{dt})=I\dfrac{d}{dt}(6t^2-12t)=I(12t-12)=0$

Then, $12t-12=0\Rightarrow t=1s$

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

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

  1. $\dfrac{A}{4}$

  2. $\dfrac{7A}{29}$

  3. $A$

  4. $\dfrac{7A}{30}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Kepler's second law states that the radius vector sweeps out equal areas in equal times. February 2012 had 29 days. The area swept in 7 days is 7/29 of the total area.

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

(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. 

  1. $(i),(iii),(iv)$ are correct

  2. $(i)$ is correct

  3. $(i),(ii)$ are correct

  4. $(iii)$ is correct
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 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

  1. X-axis

  2. Y-axis

  3. Z-axis

  4. Line at equal angles to all the three axes
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given,

$\vec r=\hat i+2\hat j-\hat k$
$\vec P=3\hat i+4\hat j-2\hat k$
Angular momentum, $\vec L=\vec r \times \vec P$
$\vec L=(\hat i+2\hat j-\hat k)\times (3\hat i+4\hat j-2\hat k)$
$\vec L=0\hat i-\hat j-2\hat k$
Hence, The angular momentum is perpendicular to the X-axis.
The correct option is A.

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 $1\ kg$ 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 

  1. $- 20\ N-m$ $ \hat{k} $

  2. $+ 20\ N-m$ $ \hat{k} $

  3. $- 60\ N-m$ $ \hat{k} $

  4. $+ 60\ N-m$ $ \hat{k} $
Reveal answer Fill a bubble to check yourself
B 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 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  

  1. zero

  2. 60 unit

  3. 7.5 unit

  4. $40\sqrt2$ unit
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

L = m * v * d, where d is the perpendicular distance from the origin to the line y = x + 4 (or x - y + 4 = 0). d = |0 - 0 + 4| / sqrt(1^2 + (-1)^2) = 4 / sqrt(2) = 2 * sqrt(2). L = 5 * (3 * sqrt(2)) * (2 * sqrt(2)) = 5 * 3 * 2 * 2 = 60.

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 angular momentum of an electron in a hydrogen atom is proprotional to ( where r is redius of orbit) 

  1. $\frac{1}{\sqrt{r}}$

  2. $\frac{1}{r}$

  3. $r^{1/2}$

  4. $^r{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Radius of the nth orbit rn ∝ n2/Z      ⇒    n ∝ (r n)½

Angular momentum Ln = nh/(2π) ∝ (r n)½

$=r^{1/2}$

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

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

  1. $mV\hat{J}$

  2. $-mVa\hat{K}$

  3. $mV\hat{K}$

  4. $mVa\hat{J}$
Reveal answer Fill a bubble to check yourself
A 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 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 -

  1. $0.25 J$

  2. $2.5\times { 10 }^{ 2 }J$

  3. $2500 J$

  4. $2.5 J$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
The rotational kinetic energy is given by
$K=\dfrac{1}{2}mr^2\omega ^2=2.5 J$. . . . .(1)
If frequency of rotation made 10 times , then the new rotational kinetic energy is
$K'=\dfrac{1}{2}mr^2 \times 10^2\omega ^2$
$K'=100K$ 
$K'=2.5\times 10^2J$
The correct option is B.