Tag: rigid body dynamics

Questions Related to rigid body dynamics

Ram says, $'A$ body may be in pure rotation in the presence of a single external force, 'Shyam says, 'This is possible only for a rigid body', then:

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. Ram's statement is correct

  2. both statements are correct in different situations

  3. both statements are wrong

  4. both statements are stated by physicists

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Correct Option: C

What torque will increase angular velocity of a solid disc of mass $16kg$ and diameter $1m$ from zero to $2$rpm in $8s$?

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. $\cfrac { \pi }{ 4 } N-m$

  2. $\cfrac { \pi }{ 2 } N-m$

  3. $\cfrac { \pi }{ 3 } N-m$

  4. $\pi N-m$

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Correct Option: D
Explanation:

Torque $\left( \tau  \right) =I\alpha $
$\tau =\cfrac { 1 }{ 2 } \times M{ R }^{ 2 }\times \cfrac { 2\pi \left( { n } _{ 2 }-{ n } _{ 1 } \right)  }{ t } $
$\therefore$ $\tau =16\times { \left( \cfrac { 1 }{ 2 }  \right)  }^{ 2 }\times \pi \cfrac { \left( 2-0 \right)  }{ 8 } =\pi N-m$

The translation distances (dx, dy) is called as

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. Translation vector

  2. Shift vector

  3. Both A and B

  4. Neither A nor B

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Correct Option: C
Explanation:

Basic theory ,$(dx,dy) $ is called as transitional or shift vector.

Rotation as well as translation motion is an example of

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. constrained motion

  2. unconstrained motion

  3. perpetual motion

  4. None of these

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Correct Option: A
Explanation:

Rotational motion and translational motion both are constrained motion.

Any point on the circumference of a rigid body which is rolling without slipping undergoes :

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. a circular path

  2. an elleptic path

  3. a cycloid path

  4. an parabolic path

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Correct Option: C
Explanation:

Any point on the rigid body, undergoing rolling without slipping, will have linear and angular speed, such that

$linear\ speed = distance\ from\ CoM \times angular\ speed$

Such particles follows cycloid path.

A common example of precession is

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. a spinning top

  2. a ball bearing

  3. a ball rolling down an inclined plane

  4. a ball sliding down an inclined plane

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Correct Option: A
Explanation:

A spinning top is a common example of precession.

Rolling without slipping is an example of

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. Rotation

  2. Translation

  3. Rotation with translation

  4. None of these

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Correct Option: C
Explanation:

When a body is rolling without slipping on the ground, its center of mass exhibits translational motion whereas the body exhibits rotational motion in its center of mass frame. Thus rolling body exhibits both translational motion as well as rotational motion.

A pendulum having a bob of mass m is hanging in a ship sailing along the equator from east to west. When the ship is stationary with respect to water, the tension in the string is $T _0$. Find the difference between tension when the ship is sailing with a velocity $v$.

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. $m v\omega$

  2. $2 mv \omega$

  3. $\displaystyle \frac{mv \omega}{2}$

  4. $\sqrt{2} m v \omega$

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Correct Option: B
Explanation:

 Additional force is Coriolis force which acts perpendicular to the plane of motion. so $\Delta T=2mv\omega $ . 

 This force causes moving objects on the surface of the Earth to be deflected to the right (with respect to the direction of travel) in the Northern Hemisphere and to the left in the Southern Hemisphere.