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 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 elastic energy properties of material substances elasticity properties of matter physics

A uniform rod of length L , area of cross-section A , mass m and Young 's modulus Y is pulled on  horizontal surface by a force f , such that the friction acting on it is F/2 . What if the elongation in the rod? 

  1. $\frac { FL }{ 2AY } $
  2. $\frac { FL }{ AY }$
  3. $\frac { 3FL }{ 2AY }$
  4. $\frac { 3FL }{ 4AY }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The tension varies along the rod due to friction. Integrating the strain along the length L with a force F and friction F/2 results in the total elongation being FL / (2AY).

Multiple choice physics upthrust in fluids, archimedes' principle and floatation density of a fluid density of fluid density and relative density

If specific gravity of the plank is 0.5. then angle $\theta $ which plank make with horizontal its equilibrium is :

  1. $\dfrac { \pi }{ 4 } $
  2. $\dfrac { 2\pi }{ 3 } $
  3. $\dfrac { \pi }{ 6 } $
  4. $\dfrac { \pi }{ 3 } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The equilibrium of a floating plank depends on the balance of buoyancy and gravity. For a plank of specific gravity 0.5, the angle theta with the horizontal is determined by the geometry of the submerged portion. The correct angle is pi/6.

Multiple choice physics friction advantages and disadvantages of friction merits and demerits of friction and methods to reduce it friction: a necessary evil

A sphere $S$ roll without slipping, moving with a constant speed on a plank $P.$ The fraction between the upper surface of $P$ and the sphere is sufficient to prevent slipping, while the lower surface of $P$ is smooth and rests on the ground. Initially, $P$ is fixed to the ground by a pin $N.$ If $N$ is suddenly removed:

  1. S will begin to slip on P

  2. P will begin to move back wards

  3. the speed of s will decrease, and its angular velocity will increase

  4. there will be no charge in the motion of S and P will still be at rest
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When the pin is removed, the sphere continues rolling without slipping because friction between the sphere and upper plank surface prevents relative motion. Since the lower surface of plank P is smooth and there's no external horizontal force on the sphere-plank system, the center of mass has no horizontal acceleration. The plank remains stationary as the sphere maintains its rolling motion.

Multiple choice physics turning effects of forces stability and centre of mass center of mass centre of mass

A solid cylinder at rest at the top of an inclined plane of height 2.7 m rolls down without slipping. If the same cylinder has to slide down a frictionless inclined plane and acquire the same velocity as that acquired by the centre of mass of the rolling cylinder at the bottom of the inclined plane, the height of the inclined plane in meters should be 

  1. 2.2

  2. 1.2

  3. 1.6

  4. 1.8
Reveal answer Fill a bubble to check yourself
C Correct answer