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

A planetary gear train has four gears and one carrier. Angular velocities of the gears are $\infty_1$,$\infty_2$,$\infty_3$ and$\infty_4$ respectively. The carrier rotates with angular velocity $\infty_5$.

For $\infty_1$= 60 rpm clockwise (cw) when looked from the left, what is the angular velocity of the carrier and its direction so that Gear 4 rotates in counterclockwise (ccw) direction at twice the angular velocity of Gear 1 when looked from the left?

  1. 130 rpm, cw

  2. 223 prm, ccw

  3. 256 rpm, cw

  4. 156 rpm, ccw
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Multiple choice

A planetary gear train has four gears and one carrier. Angular velocities of the gears are $\infty_1$,$\infty_4$,$\infty_4$ and$\infty_4$ respectively. The carrier rotates with angular velocity $\infty_4$.

What is the relation between the angular velocities of Gear 1 and Gear 4?
  1. $\begin{matrix} \ \omega_1 -\omega_5 \\ \ \omega_1 -\omega_5 \\ \end{matrix}=6$
  2. $\frac{\omega_1-\omega_5}{\omega_1\hspace{0.3cm}\omega_5}=6$
  3. $\frac{\omega_1-\omega_5}{\omega_4-\omega_5}=-\bigg(\frac{2}{3}\bigg)$
  4. $\frac{\omega_1-\omega_5}{\omega_4-\omega_5}=\frac{8}{9}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\frac{\omega_1-\omega_5}{\omega_4-\omega_5}=\frac{x}{x\times\frac{Z_1Z_3}{Z_2Z_4}}=\frac{Z_2Z_4}{Z_1Z_3}\\ \frac{\omega_1-\omega_5}{\omega_4-\omega_5}=\frac{45\times40}{15\times20}=3\times2=6$

Multiple choice

A uniform, slender cylindrical rod is made of a homogeneous and isotropic material. The rod rests on a frictionless surface. The rod is heated uniformly. If the radial and longitudinal thermal stresses are represented by $\sigma_r$ and $\sigma_z$, respectively, then
  1. $\sigma_r=0,\sigma_z=0$
  2. $\sigma_r\neq0,\sigma_z=0$
  3. $\sigma_r=0,\sigma_z\neq0$
  4. $\sigma_r\neq0,\sigma_z\neq0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\text {We know that due to temperature changes, dimensions of the material change.}\\ \text{ If these changes in the dimensions are prevented partially or fully,stresses are generated in the material and if the changes in the dimensions are not prevented, there will be no stress set up.(Zero stresses).}\\ \text{ Hence cylindrical rod is allowed to expand or contract freely.} \\ So \sigma_r=0and \sigma_z=0$

Multiple choice

An instantaneous configuration of a four-bar mechanism, whose plane is horizontal, is shown in the figure below. At this instant, the angular velocity and angular acceleration of link O2A are $\omega8red/s$ and$\alpha=0$, respectively, and the driving torque $(t)$ is zero. The link O2A is balanced so that its center of mass falls at O2.

At the instant considered, what is the magnitude of the angular velocity of O4B?

  1. 1 rad/s

  2. 3 rad/s

  3. 8 rad/s
  4. $\frac{64}{3}red/s$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\text{Let,w_4 is the angular velocity of link $O_4$B}\\ \text{From the triangle ABC,}\\ \hspace{2cm}tan\theta=\frac{100}{240}=\frac{5}{12}\hspace{6cm}...(i)\\ \theta=tan^{-1}(\frac{5}{12})=22.62^0 \\ \text{Also from the triangleO_1O_2A,}$

Multiple choice

An instantaneous configuration of a four-bar mechanism, whose plane is horizontal, is shown in the figure below. At this instant, the angular velocity and angular acceleration of link O2A are $\omega8red/s$ and $\alpha=0$, respectively, and the driving torque $(t)$ is zero. The link O2A is balanced so that its center of mass falls at O2.

Which kind of 4-bar mechanism is O2 ABO4?

  1. Double-crank mechanism

  2. Crank-rocker mechanism

  3. Double-rocker mechanism

  4. Parallelogram mechanism
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Multiple choice

An instantaneous configuration of a four-bar mechanism, whose plane is horizontal, is shown in the figure below. At this instant, the angular velocity and angular acceleration of link O2A are $\omega8red/s$ and$\alpha=0$, respectively, and the driving torque $(t)$ is zero. The link O2A is balanced so that its center of mass falls at O2.

At the same instant, if the component of the force at joint A along AB is 30 N, then the magnitude of the joint reaction at O2

  1. is zero

  2. is 30 N

  3. is 78 N

  4. cannot be determined from the given data
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

From the given data the component of force at joint A along $AO_2$ is necessary to find the joint reaction at $O_2$. So, it is not possible to find the magnitude of the joint reaction at $O_2$

Multiple choice friction laws of motion physics

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:

  1. $10\ cm$
  2. $20\ cm$
  3. $40\ cm$
  4. $80\ cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

It slips when.
$\mu mg = m{\omega ^2}r$
$ \Rightarrow \mu g = {\omega ^2}r$
$ \Rightarrow \mu g = {\omega ^2}40 - \left( 1 \right)$
$Now,\,\omega  = 2\omega $
$ \Rightarrow \mu g = {\left( {2\omega } \right)^2}r \Rightarrow 4{\omega ^2}r - \left( 2 \right)$
$\therefore {\omega ^2} \times 40 = 4{\omega ^2}r$
$ \Rightarrow r = 10cm$

Multiple choice friction laws of motion physics

A solid cylinder is placed on a rough inclined surface of inclination $\theta$. Minimum value of coefficient of static friction between the cylinder and the surface so that the cylinder rolls without slipping is

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

For a solid cylinder to roll without slipping on an incline, the friction force f = (1/3)mg*sin(theta). The condition f <= mu*N = mu*mg*cos(theta) leads to mu >= (1/3)tan(theta).

Multiple choice physics hooke's law

An elastic metal rod will change its length when it

  1. falls vertically under its weight

  2. is pulled along its length by a force acting at one end

  3. rotates about an axis at one end

  4. slides on a rough surface
Reveal answer Fill a bubble to check yourself
B,C Correct answer
Explanation

An elastic metal rod will change its length when it is pulled along its length by a force acting at one end or rotates about an axis at one end. Since, deforming force exceeds the elastic limit.

Multiple choice motional emf physics

A non conducting ring having charge q uniformly distributed over its circumference is placed on a rough horizontal surface. A vertical time varying magnetic field $B=4t^2$ is switched on a time $t=0$. Mass of the ring is m and radius is R. The ring starts rotating after $2$ seconds. The coefficient of friction between the ring and the tablets.

  1. $\displaystyle\frac{4qmR}{g}$
  2. $\displaystyle\frac{2qmR}{g}$
  3. $\displaystyle\frac{8qR}{mg}$
  4. $\displaystyle\frac{qR}{2mg}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice physics simple harmonic motion representing shm with circular motion shm as projection of circular motion simple harmonic motion (shm) as a projection of uniform circular motion

The circular motion of a particle whose speed is constant is

  1. Periodic but not simple harmonic

  2. Simple harmonic but not periodic

  3. Periodic and simple harmonic

  4. Neither periodic not simple harmonic
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Uniform circular motion is a periodic motion but not simple harmonic

The correct option is (a)

Multiple choice physics simple harmonic motion representing shm with circular motion shm as projection of circular motion simple harmonic motion (shm) as a projection of uniform circular motion

To understand Simple Harmonic Motion as analogous to circular motion,

  1. we project the circular motion of the particle along any radius.

  2. we project the circulation motion of the particle along a chord.

  3. we project the circulation motion of the particle along the diameter.

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

The circular motion can be resolved into a S.H.M. In this process we project circular motion of particle along diameter the projection of particle performs S.H.M. with centres as mean positions.

Multiple choice physics simple harmonic motion representing shm with circular motion shm as projection of circular motion simple harmonic motion (shm) as a projection of uniform circular motion

Simple harmonic motion is the projection of uniform circular motion on the

  1. $x$- axis
  2. $y$- axis

  3. reference circle

  4. any diameter of reference circle.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple harmonic motion is the projection of uniform circular motion on any diameter of reference circle.