Physics

Rotational and Circular Motion

220 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 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
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

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

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

If a person sitting on a rotating stool with his hands outstretched, suddenly lowers his hands, then his :

  1. Kinetic energy will decrease.

  2. Moment of inertia will decrease.

  3. Angular momentum will increase.

  4. Angular velocity will remain constant.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to conservation of Angular Momentum,
$I \omega$ = constant
Hence, when a person sitting on a rotating stool suddenly  lowers his hands, then his angular velocity will increase and moment of inertia will decrease. 

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 man spinning in free space changes the shape of his body, eg. by spreading his arms or curling up. By doing this, he can change his :

  1. moment of inertia

  2. angular momentum

  3. angular velocity

  4. rotational kinetic energy
Reveal answer Fill a bubble to check yourself
A,C,D Correct answer
Explanation

The moment of inertia can be increased or angular velocity can be decreased by stretching hands outside. Also, smaller the moment of inertia means less resistance to rotation (some rapid corrections have to made to achieve rotational equilibrium), hence change in moment of inertia leads the change in rotational kinetic energy. While angular momentum remains conserved.

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 particles are initially moving with angular momentum $\vec{L _{1}}$ and $\vec{L _{2}}$ in a region of space with no external torque. A constant external torque $\vec{\tau}$ then acts on one particle, but not on the other particle, for a time interval $\Delta{t}$. What is the change in the total angular momentum of the two particles?

  1. $\vec\Delta L=\vec {L _{1}}-\vec{L _{2}}$
  2. $\Delta L=\dfrac{1}{2}(\vec {L _{1}}-\vec{L _{2}})$
  3. $\vec\Delta L=\tau \Delta t$
  4. $\vec\Delta L$ is not applicable for this system.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The change in angular momentum is equal to the impulse of the torque, which is torque multiplied by time (delta L = tau * delta t).

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

uniform disc of mass M and radius R is rotating about its centre of mass (the centre of mass is at rest )with an angular speed $\omega $.the angular momentum of disc about a point A (as shown)will be.

  1. $M{R^2}\omega + MhR\omega $
  2. $\frac{1}{2}M{R^2}\omega $
  3. $\frac{1}{2}M{R^2}\omega + MhR\omega $
  4. $\frac{1}{2}M{R^2}\omega + 1/2MhR\omega $
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

when a mass is rotating in a plane about a fixed point, its angular momentum is directed along

  1. radius

  2. the tangent to the orbit

  3. a line perpendicular to the plane of rotation

  4. none of above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Angular momentum is defined as the cross product of the position vector and linear momentum. For a mass rotating in a plane, the direction of this vector is determined by the right-hand rule, which is always perpendicular to the plane of rotation.

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
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

 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

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

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
B Correct answer