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If the angular momentum of a rotating body about a fixed axis is increased by $10 %,$ then its kinetic energy will be increased by

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Important Questions on Systems of Particles and Rotational Motion

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Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

A solid sphere of mass,

m

and radius,

R

is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation

(\frac{E_{sphere}}{E_{cylinder}})

will be

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy

(K_{t})

as well as rotational kinetic energy

(K_{r})

simultaneously. The ratio

K_{t} : (K_{t} + K_{r})

for the sphere is

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

A uniform solid cylindrical roller of mass

m

is being pulled on a horizontal surface with force

F

parallel to the surface and applied at its centre. If the acceleration of the cylinder is

a

and it is rolling without slipping then the value of

F

is:

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

In a physical balance working on the principle of moments, when

5 mg

weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

A uniform circular disc of radius

50 cm

at rest is free to rotate about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of

2.0 r a d s^{- 2}

. Its net acceleration in

m s^{- 2}

at the end of

2.0 s

is approximately:

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

A uniform disc of radius

R

and mass

M

is free to rotate only about its axis. A string is wrapped over its rim and a body of mass

m

is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is:

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MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

A rod of length $50 c m$ is pivoted at one end. It is raised such that it makes an angle of $30^{o}$ from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in $r a d s^{- 1}$ ) will be $(g = 10 m s^{- 2})$

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MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to:

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Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

Three objects,

A

: (a solid sphere),

B

: (a thin circular disk) and

C

: (a circular ring), each have the same mass

M

and radius

R

. They all spin with the same angular speed

ω

about their own symmetric axes. The amounts of work

(W)

required to bring them to rest, would satisfy the relation

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

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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Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

Two discs of same moment of inertia

(I)

are rotating in same sense about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities

ω_{1}

and

ω_{2}

. They are brought into contact face to face coinciding the axis of rotation. The expression for loss in energy during this process is

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

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?

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

A cylinder of mass M_c and sphere of mass M_s are placed at points A and B of two inclines, respectively. (See figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio

\frac{sin θ_{c}}{sin θ_{s}}

is :

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Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

A solid sphere of mass

2 kg

is rolling on a frictionless horizontal surface with velocity

6 m s^{- 1}

. It collides on the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be (Force constant of the spring =

36 N m^{- 1}

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration 'a' perpendicular to the axis of the cylinder. What is F_friction at point P ? It is assumed that the cylinder does not slip.
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MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $h_{s p h}$ and $h_{c y l}$ on the incline. The ratio $\frac{h_{s p h}}{h_{c y l}}$ is given by:
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Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

A disc of radius

2 m

and mass

100 k g

rolls on a horizontal floor. Its centre of mass has speed of

20 c m s^{- 1} .

How much work is needed to stop it?

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

A homogeneous solid cylindrical roller of radius

R

and mass

M

is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is:

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Energy in Rotation

The moment of inertia of a ring about an axis passing through the centre and perpendicular to its plane is

I

. It is rotating with angular velocity

ω.

Another identical ring is gently placed on it so that their centres coincide. If both the rings are rotating about the same axis then loss in kinetic energy is

If the angular momentum of a rotating body about a fixed axis is increased by 10%, then its kinetic energy will be increased by

Important Questions on Systems of Particles and Rotational Motion

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If the angular momentum of a rotating body about a fixed axis is increased by $10 %,$ then its kinetic energy will be increased by