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 turning on a pivot the turning of couple couple turning effect of force the turning effect of a force moment of force or torque

The minimum value of ${ \omega  } _{ 0 }$ below which the ring will drop down is 

  1. $\sqrt { \dfrac { g }{ 2\mu (R-r) } } $
  2. $\sqrt { \dfrac { 3g }{ 2\mu (R-r) } } $
  3. $\sqrt { \dfrac { g }{ \mu (R-r) } } $
  4. $\sqrt { \dfrac { 2g }{ \mu (R-r) } } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This relates to the critical angular velocity required for a ring to maintain contact or prevent slipping in a rotating system. The derivation leads to the expression in option C.

Multiple choice physics turning on a pivot the turning of couple couple turning effect of force the turning effect of a force moment of force or torque

Two discs having masses in the ratio $1:2$ and radii in the ratio $1:8$ roll down without slipping one by one from an inclined plane of height $h$. The ratio of their linear velocities on reaching the ground is

  1. $1:16$
  2. $1:128$
  3. $1:8\sqrt{2}$
  4. $1:1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a disc rolling down an incline, the final linear velocity v = sqrt(2gh / (1 + k^2/R^2)). For a uniform disc, k^2/R^2 = 0.5. Since the velocity depends only on height h and the shape (moment of inertia factor), the mass and radius do not affect the final velocity. Thus, the ratio is 1:1.

Multiple choice physics types of energy law of conservation of energy the law of conservation of energy work, energy and machines

A stone of mass $m$ kg is whirled in a vertical circle of radius $20$ cm. The difference in the kinetic energies at the lowest and the topmost position is:

  1. $4 \ mg\ joule$
  2. $0.4\ mg\ joule$
  3. $40 \ mg \ joule$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to the law of conservation of energy 
Total energy of the system (KE $+$ PE) will be equal at both  , topmost and bottom most point.
Therefore, $\bigtriangleup PE =\bigtriangleup KE$
 $KE _{b}-KE _{t} = PE _{t} - PE _{b}$
$PE _{t} - PE _{b} = m\times g\times (2\times r)$
$\bigtriangleup KE = 0.4 \ mg$ $joule$

Multiple choice newton's colour disc light and the formation of shadows physics

When the Newton's disc is rotated what happens

  1. The colours fade to white

  2. The colours fade to black

  3. The colours fade to red

  4. The colours fade to blue
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Newton's colour disc, as the name suggests, was invented by Sir Issac Newton and is a disc with seven segments in rainbow colours.
When the disc is rotated, the colours fade to white. In this way, Sir Isaac Newton demonstrated that white light is a combination of the seven different colours found in a rainbow.

Hence, the correct answer is OPTION A.

Multiple choice physics rotational motion of a rigid body and moment of inertia motion of rigid body rigid body equilibrium of a rigid body

A uniform sphere is placed on a smooth horizontal surface and a horizontal force $F$ is applied on it at a distance $'h'$ above the surface. The acceleration of the centre

  1. Is maximum when $h=0$
  2. Is maximum when $h=\dfrac { 2R }{ 5 }$
  3. Is maximum when $h=\dfrac { 7 }{ 5 } R$
  4. Is independent of $h$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a sphere on a smooth surface, the acceleration of the center of mass is given by a = F/m, according to Newton's second law. This value is independent of the point of application 'h'.

Multiple choice physics rotational motion of a rigid body and moment of inertia motion of rigid body rigid body equilibrium of a rigid body

Assertion (A) : A wheel may be rotated with uniform angular velocity even though the tangential forces are applied on it.
Reason (R) : Angular acceleration of wheel is zero when tangential force and frictional force produce torques equal in magnitude and opposite in direction.

  1. Both A and R are true and R is correct explanation of A

  2. Both A and R are true and R is not correct explanation of A

  3. A is true and R is false

  4. A is false and R is true
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A wheel is rotated with uniform angular velocity even if the tangential force is applied it happens only if a counter torque is acted on the wheel to balance the torque of the applied force. The $ angular$ $ acceleration $ of the wheel is $ zero$ if the torque of the tangential force is balanced by any other force $(i.e. friction)$.

Multiple choice physics rotational motion of a rigid body and moment of inertia motion of rigid body rigid body equilibrium of a rigid body

A body is in pure rotation. The linear speed $v$ of the particle, the distance $r$ of the particle from the axis and the angular velocity $\omega$ of the body are related as $\omega=\dfrac{v}{r}$. Thus

  1. $\omega \propto \dfrac{1}{r}$
  2. $\omega \propto r$
  3. $v$
  4. $\omega$ $is\ independent\ of$ $r$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The relationship v = omega * r implies that for a constant linear speed v, omega is inversely proportional to r (omega = v/r).

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

When a spinning top slows down, it begins to wobble. This phenomenon can be explained by

  1. gyroscopic precession

  2. inertia of motion

  3. force of gravity

  4. more complicated types of motion are coming into play
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When the top slows down, air bouancy, gravitational force, inertial movement and other complicated motion concepts act on it resulting into wobbling of the top.

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

Which of the following statements can be suitable?

  1. Rotational motion is a type of circular motion.

  2. Circular motion is similar to rotational motion.

  3. Rotational and circular motion are fundamentally unrelated.

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In circular motion, the body revolves around a certain axis. So that body posses a certain angular velocity, angular acceleration and frequency of rotation where these terms are used in rotational motion. Thus circular motion is said to be similar to rotational motion.

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

A man stands at the centre of a turn table it extended horizontally, with a $5 kg$ mass hand. He is set into rotation with an angular of one revolution in $2s$. His new angular is he drops his hands to his sides is (Assume moment of inertia of the man is $6 \ kgm^2$. The distance of the wavelength from the axis is $1 m$and final distance is $0.2 m$)

  1. $2.5 \ rev/s$
  2. $1.25 \ rev/s$
  3. $5 \ rev/s$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

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

  1. $\cfrac { \pi }{ 4 } N-m$
  2. $\cfrac { \pi }{ 2 } N-m$
  3. $\cfrac { \pi }{ 3 } N-m$
  4. $\pi N-m$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 } $
$\therefore$ $\tau =16\times { \left( \cfrac { 1 }{ 2 }  \right)  }^{ 2 }\times \pi \cfrac { \left( 2-0 \right)  }{ 8 } =\pi N-m$

Multiple choice physics turning effects of forces the turning effect of a force moment of force or torque couple

A disc is rolling on a surface without slipping. What is the ratio of its translational to rotational kinetic energies?

  1. $5:2$
  2. $2:1$
  3. $3:2$
  4. $2:3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Translational Kinetic Energy$=\cfrac{1}{2}mv^{2}=KE _{T}$
Rotational KE$=\cfrac{1}{2}I\omega^{2}$
$v=r\omega\,\,\,\,,I=\cfrac{1}{2}MR^{2}$
Rotational KE$=\cfrac{1}{2}\times\cfrac{1}{2}mR^{2}\times(\cfrac{v}{R})^{2}$
$KE _{r}=\cfrac{1}{4}mv^{2}$
$\cfrac{KE _{T}}{KE _{r}}=\cfrac{\cfrac{1}{2}mv^{2}}{\cfrac{1}{4}mv^{2}}=2:1$
Multiple choice physics turning effects of forces the turning effect of a force moment of force or torque couple

A solid sphere rolls on horizontal surface without slipping. What is the ratio of its rotational to translation kinetic energy.

  1. $\dfrac {2}{5}$
  2. $\dfrac {5}{2}$
  3. $\dfrac {3}{2}$
  4. $0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a solid sphere rolling without slipping, rotational kinetic energy is (1/2) I w^2 where I = (2/5) M R^2, and translational kinetic energy is (1/2) M v^2. Since v = w R, rotational kinetic energy is (1/5) M v^2 and translational is (1/2) M v^2. Their ratio is (1/5) / (1/2) = 2/5.