Tag: rotational motion of a rigid body and moment of inertia

Questions Related to rotational motion of a rigid body and moment of inertia

If Kinetic energy is expressed as $mv^2/2$ for a particle undergoing uniform velocity motion, How is the kinetic energy expressed in case of the same particle, if it was rotating:

physics rotational motion of a rigid body and moment of inertia constant angular acceleration equation of motion of rotating body dynamics of rotational motion about a fixed axis

  1. $m \omega^2/2$

  2. $I \omega^2/2$

  3. $m V^2/2$

  4. $I V^2/2$

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Correct Option: B
Explanation:

In rotation, m is replaced by I and v by  $\omega$. Thus the expression for kinetic energy becomes $I \omega^2/2$

The correct option is thus option (b)

A sphere rolls down on an inclined plane of inclination $\theta$. What is the acceleration as the sphere reaches bottom?

physics rotational motion of a rigid body and moment of inertia constant angular acceleration equation of motion of rotating body dynamics of rotational motion about a fixed axis

  1. $\dfrac { 5 }{ 7 } g\sin \theta$

  2. $\dfrac { 3 }{ 5 } g\sin \theta$

  3. $\dfrac { 2 }{ 7 } g\sin \theta$

  4. $\dfrac { 2 }{ 5 } g\sin \theta$

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Correct Option: A
Explanation:

Net force = $mg \sin \theta$

Friction force = $F (\uparrow)$
For linear motion, 
$mg \, \sin \theta = f = mg$ ...(1)
angular motion 
$fR = I \alpha $ .... (2)
$\therefore mg \, \sin \theta = ma + \dfrac{I \alpha}{R}$ ....(3)
$a = \alpha R$
$\therefore a = \dfrac{59}{7} \sin \theta$

What is the displacement of the point on the wheel initially in contact with the ground when the wheel rolls forwards half of revolution? Take the radius of the wheel as $'R'$ and the x-axis in the forward direction

physics rotational motion of a rigid body and moment of inertia constant angular acceleration equation of motion of rotating body dynamics of rotational motion about a fixed axis

  1. $R\sqrt{\pi^2 + 9}, Tan^{-1}\left(\dfrac{3}{\pi}\right)$ with x-axis

  2. $R\sqrt{\pi^2 + 4}$ and angle $Tan^{-1}\left(\dfrac{2}{\pi}\right)$ with x-axis

  3. $R\sqrt{\pi^2 + 16}, Tan^{-1}\left(\dfrac{4}{\pi}\right)$ with x-axis

  4. None

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Correct Option: B

A solid cylinder rolls down a rough inclined plane without slipping. As it goes down, what will happen due to force of friction?

physics rotational motion of a rigid body and moment of inertia constant angular acceleration equation of motion of rotating body dynamics of rotational motion about a fixed axis

  1. Decrease its mechanical kinetic energy

  2. Increase its translational energy

  3. Increases its rotational kinetic energy

  4. Decreases its potential energy

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Correct Option: C

A ball rolling off the top of a staicase of each step with height H and width W, with an initial velocity U will just hit nth step. Then n = 

physics rotational motion of a rigid body and moment of inertia constant angular acceleration equation of motion of rotating body dynamics of rotational motion about a fixed axis

  1. $\frac{2U^2H^2}{gW}$

  2. $\frac{2U^2H^2}{gW^2}$

  3. $\frac{2U^2H}{gW^2}$

  4. $\frac{2UH^2}{gW^2}$

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Correct Option: C

A small charged ball of mass m and charge q is suspended from the highers point of a ring of radius R by means of an insulated code of negligible mass.The ring is made of a rigid wire of negligible cross-section and lies in a vertical plane.On the ring, there is uniformly distributed charge Q of the same as that of q .determine the length of the cord so as the equilibrium position of the ball lies on the symmetry axis ,perpendicular to the plane of the ring. 

physics rotational motion of a rigid body and moment of inertia constant angular acceleration equation of motion of rotating body dynamics of rotational motion about a fixed axis

  1. $\left( \cfrac { 2kQqR }{ mg } \right) ^{ 1/3 }$

  2. $\left( \cfrac { kQqR }{ mg } \right) ^{ 1/3 }$

  3. $\left( \cfrac { kQqR }{ 2mg } \right) ^{ 1/3 }$

  4. $\left( \cfrac { kQqR }{ mg } \right) ^{ 3 }$

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Correct Option: D

If a spherical ball rolls on a table without slipping the fraction of its total energy associated with rotation is:

physics rotational motion of a rigid body and moment of inertia constant angular acceleration equation of motion of rotating body dynamics of rotational motion about a fixed axis

  1. $3/5$

  2. $2/7$

  3. $2/5$

  4. $3/7$

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Correct Option: C

A coin placed on a rotating turn table just slips if it is at a distance of $40$ cm from the centre if the angular velocity of the turntable is doubled, it will just slip at a distance of 

physics rotational motion of a rigid body and moment of inertia constant angular acceleration equation of motion of rotating body dynamics of rotational motion about a fixed axis

  1. 10 cm

  2. 20 cm

  3. 40 cm

  4. 80 cm

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Correct Option: C

The minimum coefficient of friction for which the sphere will have pure rolling after some time, for $\theta ={ 45 }^{ 0 }$ is

physics rotational motion of a rigid body and moment of inertia constant angular acceleration equation of motion of rotating body dynamics of rotational motion about a fixed axis

  1. $\frac { 2 }{ 7 } $

  2. $\frac { 1 }{ 7 } $

  3. $\frac { 2 }{ 5} $

  4. none of these

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Correct Option: C

A wheel whose radius is $r$ and moment of inertia about its-own axis is $I$, can rotate freely about its own horizontal axis. A rope is wrapped on the wheel. A boy of mass $m$ is suspended from the free end of the rope. The body is released from rest. The velocity of the body after falling a distance $h$ would be- 

physics rotational motion of a rigid body and moment of inertia constant angular acceleration equation of motion of rotating body dynamics of rotational motion about a fixed axis

  1. $\left(\dfrac{mgh}{I}\right)^{{1}/{2}}$

  2. $\left(\dfrac{2mgh}{m+I}^{{1}/{2}}\right)$

  3. $\left(\dfrac{2mgh}{m+I/r^2}\right)^{{1}/{2}}$

  4. $\left(\dfrac{m +I}{mgh}\right)^{{1}/{2}}$

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Correct Option: C