EASY

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A rod $A B$ of length $1 m$ is placed at the edge of a smooth table as shown. It is hit horizontally at point $' B' .$ If the displacement of center of mass in $1 s$ is $5 \sqrt{2} m .$ the angular velocity of the rod is (Take c $g = 10 m \cdot s^{- 2}$ )

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Important Questions on Systems of Particles and Rotational Motion

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A solid sphere spinning about a horizontal axis with an angular velocity

ω

is placed on a horizontal surface. Subsequently it rolls without slipping with an angular velocity of-

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

Persons $A$ and $B$ are standing on the opposite sides of a $3.5 m$ wide water stream that they wish to cross. Each one of them has a rigid wooden plank whose mass can be neglected. However, each plank is only slightly longer than, $3 m .$ So, they decide to arrange them together as shown in the figure schematically. With $B$ (the mass $17 kg$ ) standing, the maximum mass of $A$ , who can walk over the plank is close to,

Question Image

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A rope is wound around a hollow cylinder of mass

3 kg

and radius

40 cm.

What is the angular acceleration of the cylinder if the rope is pulled with a force of

30 N

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A solid cylinder of mass

50 k g

and radius

0.5 m

is free to rotate about horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of

2

revolutions

s^{- 2}

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A particle of mass

20 g

is released with an initial velocity

5 m s^{- 1}

along the curve from the point

A,

as shown in the figure. The point

A

is at height

h

from point

B .

The particle slides along the frictionless surface. When the particle reaches point

B,

its angular momentum about

O

will be: (Take

g = 10 m s^{- 2}

)

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A solid cylinder of mass

2 k g

and radius

4 c m

is rotating about its axis at the rate of

3 rpm

. The torque required to stop after

2 π

revolutions is

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A wheel of radius, $R$ with an axle of radius, $\frac{R}{2}$ is as shown in the figure and is free to rotate about a frictionless axis through its center and perpendicular to the page. Three forces $(F, F, 2 F)$ , are exerted tangentially to the respective rims as shown in the figure.

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The magnitude of the net torque acting on the system is nearly,

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A particle is moving uniformly along a straight line as shown in the figure. During the motion of the particle from $A$ to $B$ , the angular momentum of the particle about ${}^{'}O^{'}$

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MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A slender uniform rod of mass

M

and length

l

is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle

θ

with the vertical is:

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HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A disc of the moment of inertia

I_{1}

is rotating in a horizontal plane about an axis passing through a centre and perpendicular to its plane with constant angular speed

ω_{1}

Another disc of the moment of inertia

I_{2}

having zero angular speed is placed coaxially on a rotating disc. Now both the disc are rotating with the constant angular speed

ω_{2}

. The energy lost by the initial rotating disc is

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A metal coin of mass

5 g

and radius

1 c m

is fixed to a thin stick

A B

of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about

A B

25

rotations per second in

5 s

, is close to:
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MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

The moment of the force,

\vec{F} = 4 \hat{i} + 5 \hat{j} - 6 \hat{k}

(2, 0, - 3),

about the point

(2, - 2, - 2),

is given by

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A particle of mass

m

is moving along a trajectory given by

x = x_{0} + a c o s ω_{1} t

y = y_{0} + b s i n ω_{2} t

The torque, acting on the particle about the origin, at

t = 0

is:

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

The time dependence of the position of a particle of mass

m = 2

is given by

\vec{r} (t) = 2 t \hat{i} - 3 t^{2} \hat{j}

. Its angular momentum, with respect to the origin, at time

t = 2

is:

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

Three point masses each of mass

m

are kept at the corners of an equilateral triangle of side

L

. The system rotates about the center of the triangle without any change in the separation of masses during rotation. The period of rotation is directly proportional to

(\cos 30 ° = s i n 60 ° = \frac{\sqrt{3}}{2})

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius

R_{e} .

By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become

\sqrt{\frac{3}{2}}

times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is

R

. Value of

R

is :

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A solid sphere of radius

r

is revolving about one of its diameters with an angular velocity

ω .

If it suddenly expands uniformly so that its radius increases to

n

times its original value, then its angular velocity becomes

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A uniform bar of mass $M$ is supported by a pivot at its top about which the bar can swing like a pendulum. If a force $F$ is applied perpendicular to the lower end of the bar as shown in figure, what is the value of $F$ in order to hold the bar in equilibrium at an angle $(θ)$ from the vertical

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MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

To mop-clean a floor, a cleaning machine presses a circular mop of radius

R

vertically down with a total force

F

and rotates it with a constant angular speed about its axis. If the force

F

is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is

μ,

the torque, applied by the machine on the mop is:

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A force of

40 N

acts on a point

B

at the end of an L-shaped object as shown in the figure. The angle

θ

that will produce the maximum moment of the force about point

A

is given by:
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A rod AB of length 1 m is placed at the edge of a smooth table as shown. It is hit horizontally at point 'B'. If the displacement of center of mass in 1 s is 52 m. the angular velocity of the rod is (Take cg=10 m·s-2)

Important Questions on Systems of Particles and Rotational Motion

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A rod $A B$ of length $1 m$ is placed at the edge of a smooth table as shown. It is hit horizontally at point $' B' .$ If the displacement of center of mass in $1 s$ is $5 \sqrt{2} m .$ the angular velocity of the rod is (Take c $g = 10 m \cdot s^{- 2}$ )