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What is the difference between translational and rotational motion?

Important Questions on Systems of Particles and Rotational Motion

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Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

A uniform solid sphere of radius

R

and radius of gyration

K

about an axis passing through the centre of mass, is rolling without slipping. Then the fraction of total energy associated with its rotation will be

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

A rigid massless rod of length $3 l$ has two masses attached at each end as shown in the figure. The rod is pivoted at point $P$ on the horizontal axis. When released from the initial horizontal position, its instantaneous angular acceleration will be

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MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

A ball is rolling without slipping in a spherical shallow bowl (radius $R$ ) as shown in the figure and is executing simple harmonic motion. If the radius of the ball is doubled, then the time period of oscillation

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HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

A cylinder of mass,

m

is allowed to roll on a smooth horizontal table with a spring of spring constant,

k

attached to it so that it executes SHM about the equilibrium position. What is the time period,

T

of oscillations?

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

V -

shaped rigid body has two identical uniform arms. What must be the angle between the two arms, so that when the body is hung from one end the other arm is horizontal?

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

In a uniform circular motion

\vec{r}, \vec{V}

and

\vec{ω}

stands for radius vector, linear velocity and angular velocity respectively. Then which of the following is true?

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

A particle of mass

10 g

moves along a circle of radius

6.4 cm

with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to

8 \times 10^{- 4} J

by the end of the second revolution after the beginning of the motion?

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

A solid sphere rolls without slipping, first horizontally and then up to a point $x$ at height $h$ on an inclined plane before rolling down, as shown in the figure below.

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The initial horizontal speed of the sphere is

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

A rigid ball rolls without slipping on a surface shown below.

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Which on the following is the most likely representation of the distance travelled by the ball vs time graph?

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

A solid cylinder P rolls without slipping from rest down an inclined plane attaining a speed

v_{P}

at the bottom. Another smooth solid cylinder

Q

of same mass and dimensions slides without friction from rest down the inclined plane attaining a speed

v_{Q}

at the bottom. The ratio of the speeds

(\frac{v_{Q}}{v_{P}})

is -

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

A wheel of radius "rolls without slipping with a speed $v$ on a horizontal road. When it is at a point $A$ on the road a small bob of the mud separates from wheel at the highest point and touches the point $B$ on the road as shown in the figure. Then $A B$ is (g-acceleration due to gravity)

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HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

On a pulley of mass $M$ hangs a rope with two masses $m_{1}$ and $m_{2} (m_{1} > m_{2})$ tied at the ends as shown in the figure. The pulley rotates without any friction, whereas the friction between the rope and the pulley is large enough to prevent any slipping. Which of the following plots best represents the difference between the tensions in the rope on the two sides of the pulley as a function of the mass of the pulley?

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MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

Consider two uniform discs of the same thickness and different radii

R_{1} = R

and

R_{2} = α R

made of the same material. If the ratio of their moments of inertia

I_{1}

and

I_{2}

, respectively, about their axes is

I_{1} : I_{2} = 1 : 16

then the value of

α

is :

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

The radius of gyration of a body about an axis at a distance 6 cm from its centre of mass is 10 cm. Then its radius of gyration about a parallel axis through its centre of mass will be

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

Select the wrong statement -

Statement-I : A body may be in pure rotation under the action of single external force.

Statement-II : If a body is in pure rotation under action of single external force then it must not be rigid.

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

A body of mass

m

slides down an incline and reaches the bottom with a velocity.

v

. If the same mass were in the form of a ring which rolls down this incline. The velocity of the ring at the bottom would have been

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

In the figure $A$ and $B$ are identical blocks, each of mass $m$ and $C$ is a circular disc of equal mass $m$ . Pulley is massless and ffictionless and thread is inextensible. Neglecting friction, find the acceleration of block $A$ and $B$ .
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EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

The moment of inertia of a body about a given axis is

1.2 kg m^{2}

. Initially, the body is at rest. In order to produce rotational kinetic energy of

1500 J

, the angular acceleration of

25 rad s^{- 2}

must be applied about the axis for a duration of

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

A rigid body is in pure rotation, that is undergoing fixed axis rotation. Then which of the following statements are true -

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Rigid Body

A light thread has been tightly wrapped around a disc of mass $M$ and radius $R$ . The disc has been placed on a smooth table, lying flat as shown. The other end of the string has been attached to a mass $m$ as shown. The system is released from rest. Find the acceleration of the disc and block.
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What is the difference between translational and rotational motion?

Important Questions on Systems of Particles and Rotational Motion

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