A particle of mass m is moving along the side of a square of side 'a', with a uniform speed υ in the x-y plane as shown in the figure: Which of the following statements is false for the angular momentum L → about the origin?

L → = m υ 2 R k ^ when the particle is moving from D to A.

L → = m υ R 2 + a k ^ when the particle is moving from B to C.

L → = - m υ 2 R k ^ when the particle is moving from A to B.

L → = m υ R 2 + a k ^ when the particle is moving from C to D.

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Equivalent to force in linear motion, in rotational motion is :

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Important Questions on Rotational Mechanics

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Physics>Mechanics>Rotational Mechanics>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,

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MEDIUM

Physics>Mechanics>Rotational Mechanics>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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Physics>Mechanics>Rotational Mechanics>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>Rotational Mechanics>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:

HARD

Physics>Mechanics>Rotational Mechanics>Torque

A hoop of radius

r

and mass

m

rotating with an angular velocity

ω_{0}

is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

EASY

Physics>Mechanics>Rotational Mechanics>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

HARD

Physics>Mechanics>Rotational Mechanics>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>Rotational Mechanics>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>Rotational Mechanics>Torque

A particle of mass $2 kg$ is on a smooth horizontal table and moves in a circular path of radius $0.6 m$ . The height of the table from the ground is $0.8 m$ . If the angular speed of the particle is $12 rad s^{- 1}$ , the magnitude of its angular momentum about a point on the ground right under the center of the circle is:

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Physics>Mechanics>Rotational Mechanics>Torque

A bob of mass m attached to an inextensible string of length

l

is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed

ω

rad/s about the vertical. About the point of suspension :

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Physics>Mechanics>Rotational Mechanics>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-

HARD

Physics>Mechanics>Rotational Mechanics>Torque

An automobile moves on a road with a speed of

54 k m h^{- 1}

. The radius of its wheels is

0.45 m

and the moment of inertia of the wheel about its axis of rotation is

3 k g m^{2}

. If the vehicle is brought to rest in

15 s

, the magnitude of average torque transmitted by its brakes to the wheel is:

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Physics>Mechanics>Rotational Mechanics>Torque

A ball of mass

160 g

is thrown up at an angle of

60 °

to the horizontal at a speed of

10 m s^{- 1}

. The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly

(g = 10 m s^{- 2})

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Physics>Mechanics>Rotational Mechanics>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,

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Physics>Mechanics>Rotational Mechanics>Torque

A particle of mass m is moving along the side of a square of side 'a', with a uniform speed

υ

in the x-y plane as shown in the figure:

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Which of the following statements is false for the angular momentum

\vec{L}

about the origin?

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Physics>Mechanics>Rotational Mechanics>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}

MEDIUM

Physics>Mechanics>Rotational Mechanics>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:

EASY

Physics>Mechanics>Rotational Mechanics>Torque

Two rotating bodies,

A

and

B

of masses,

m

and

2 m

with moments of inertia

I_{A}

and

I_{B} (I_{B} > I_{A})

have equal kinetic energy of rotation. If,

L_{A}

and

L_{B}

be their angular momenta, respectively, then,

HARD

Physics>Mechanics>Rotational Mechanics>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}

)

EASY

Physics>Mechanics>Rotational Mechanics>Torque

A force

\vec{F} = α \hat{i} + 3 \hat{j} + 6 \hat{k}

is acting at a point

\vec{r} = 2 \hat{i} - 6 \hat{j} - 12 \hat{k}

. The value of

α

for which angular momentum about origin is conserved is:

Equivalent to force in linear motion, in rotational motion is :

Important Questions on Rotational Mechanics

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