Physics

Rotational and Circular Motion

235 Questions

Rotational and circular motion examines the dynamics of objects moving in circular paths or rotating around an axis. Key concepts include angular momentum, torque, moment of inertia, and centripetal force. This is a highly scoring topic in the physics section of competitive exams.

Angular momentumCentripetal forceMoment of inertiaRolling objectsGyroscopic effect

Rotational and Circular Motion Questions

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

The speed of the wave travelling on the uniform circular hoop of string, rotating clockwise in absence of gravity with tangential speed $v _0$, is :

  1. $v=v _0$
  2. $v=2v _0$
  3. $v=\dfrac{v _0}{\sqrt 3}$
  4. $v=\dfrac{v _0}{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a string rotating in a circle, the wave speed relative to the string is v0. In the absence of gravity, the speed of a transverse wave on a rotating hoop is equal to the tangential speed v0.

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 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 

  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
Reveal answer Fill a bubble to check yourself
C Correct answer
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, $j \times i = - k$
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 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?

  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
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

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

  1. Only angular $( \theta, \omega, \alpha)$

  2. Only linear (s,v,a)

  3. Both linear and angular

  4. None of them
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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 law of conservation of angular momentum is obtained from Newton's II law in rotational motion when:

  1. External torque is maximum

  2. External torque is minimum

  3. External torque is zero

  4. External torque is constant
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Newton's 2nd law says that External Force is directly proportional to the rate of change of momentum. Similarly, external torque is directly proportional to the rate of change of angular momentum. So if angular momentum is conserved i.e., the rate of change of angular momentum is zero then external torque is zero.

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

Four particles of masses in the ratio 1:2:3:4 are rotating in concentric circles of radii proportional to their masses with the same angular velocity. What is the angular momentum of the system

  1. $4mw^2r$
  2. $10mw^2r$
  3. $30mw^2r$
  4. $20mw^2r$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The angular momentum of a single particle is $mw^2r$. If there are 4 particles, we can write,
$L _{tot}=mw^2r+2mw^2(2r)+3mw^2(3r)+4mw^2(4r)=30mw^2r$

The correct option is (c)

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 identical particles of mass m move in a circle of radius r , 180 degrees out of phase at an angular speed  $\omega$ about the z-axis in a plane parallel to but a distance h above the x-y plane (Figure 19.14). Find the magnitude and the direction of the angular momentum L relative to the origin.

  1. $2mr^2w$
  2. $mr^2w$

  3. zero
  4. $mr^2w/2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For two particles at distance r from the z-axis, 180 degrees apart, the angular momentum about the origin (z-axis) is L = 2 * mvr = 2 * mr(rw) = 2mr^2w.

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 identical particles of mass m are separated by a distance of 1 metre each and are rotating with a constant speed of 5 m/s . What will be their angular momentum about an axis distant 0.8 m from the first particle on the line joining them

  1. 5m

  2. 3m

  3. 2m

  4. m
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 is in uniform circular motion in a   horizontal plane. Its angular momentum is constant when the origin is taken at

  1. centre of the circle

  2. any point on the circumference of the circle.

  3. any point inside the circle.

  4. any point outside the circle.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For uniform circular motion, the angular momentum L = r x p is constant only when the origin is at the center of the circle, as r and p are perpendicular and their magnitudes are constant.

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

(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