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A runner completes one round of a circular path of radius $r$ in $40$ seconds. His displacement after $2$ minutes $20$ seconds will be

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Important Questions on Rotational Dynamics

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Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

Two particles

A

and

B

are moving in uniform circular motion in concentric circles of radii

r_{A}

and

r_{B}

with speed

v_{A}

and

v_{B}

, respectively. Their time period of rotation is the same. The ratio of angular speed of

A

to that of

B

will be,

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Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

In non-uniform circular motion, the ratio of tangential to radial acceleration is (

r =

radius of the circle,

u =

speed of the particle,

α =

angular acceleration)

HARD

Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

A particle is moving in a circular path of radius a under the action of an attractive potential

U = - \frac{k}{2 r^{2}} .

Its total energy is:

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Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

A disc spinning at the rate

27.5

rad

s^{- 1}

is slowed at the rate 10 rad

s^{- 2}

. The time after which it will come to rest is

MEDIUM

Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

A ceiling fan rotates about its own axis with some angular velocity. When the fan is switched off, the angular velocity becomes

{(\frac{1}{4})}^{th}

of the original in time

t

and

n

revolutions are made in that time. The number of revolutions made by the fan during the time interval between switch off and rest are (Angular retardation is uniform)

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Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

A particle is performing uniform circular motion along the circumference of a circle of diameter

50 cm

with frequency

2 Hz

. The acceleration of the particle in

m s^{- 2}

is:

HARD

Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the

n^{t h}

power of R. If the period of rotation of the particle is T, then:

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Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

A wheel starting from rest gains an angular velocity of

10 rad s^{- 1}

after being uniformly accelerated for

5 \sec

. The total angle through which it has turned is

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Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

Two parallel discs are connected by a rigid rod of length $L = 0.5 m$ centrally. Each disc has a slit oppositely placed as shown in the figure. A beam of neutral atoms is incident on one of the discs axially at different velocities $v$ , while the system is rotated at angular speed of, $600 rev s^{- 1}$ , so that atoms only with a specific velocity emerge at the other end. Calculate the two largest speeds (in meter/second) of the atoms that will emerge at the other end.

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Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

Two cars

S_{1}

and

S_{2}

are moving in coplanar concentric circular tracks in the opposite sense with the periods of revolution

3 \min

and

24 \min

, respectively. At the time

t = 0,

the cars are the farthest apart. Then, the two cars will be,

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Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

A clock has a continuously moving second's hand of $0.1 m$ length. The average acceleration of the tip of the hand (in units of $m s^{- 2}$ ) is of the order of :

MEDIUM

Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

A particle at a distance of

1 m

from the origin starts moving such that

\frac{d r}{d θ} = r,

where

(r, θ)

are polar coordinates. Then the angle between resultant velocity and tangential velocity component is:

EASY

Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

The angular speed of the wheel of a vehicle is increased from,

360 rpm

1200 rpm

14 s

. Its angular acceleration is,

HARD

Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

A uniform rod of length

l

is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is

T (x)

at a distance

x

from the axis, then which of the following graphs depicts it most closely?

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Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

A body moving along a circular path due to a centripetal force having constant magnitude is an example of motion with ___ .

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Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

An object moves along the circle with normal acceleration proportional to

t^{α}

, where

t

is the time and is

α

a positive constant. The power developed by all the forces acting on the object will have time dependence proportional to

MEDIUM

Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

A solid body rotates with angular velocity

ω = a t \hat{i} + b t^{2} \hat{j}

where

a = 1 rad s^{- 2}

and

b = 0.5 rad s^{- 3}

and

t

is in seconds. Calculate the angle between the vectors of the angular velocity and the angular acceleration at

t = 1 \sec

EASY

Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

A car goes around uniform circular track of radius

R

at a uniform speed

v

once in every

T

seconds. The magnitude of the centripetal acceleration is

a_{c}

. If the car now goes uniformly around a larger circular track of radius

2 R

and experiences a centripetal acceleration of magnitude

8 a_{c}

. Then, its time period is

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Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

A flywheel at rest is to reach an angular velocity of

24 rad s^{- 1}

8 s

with constant angular acceleration. The total angle turned through during this interval is

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Physics>Mechanics>Rotational Dynamics>Characteristics of Circular Motion

Two particles $A, B$ are moving on two concentric circles of radii $R_{1}$ and $R_{2}$ with equal angular speed $ω .$ At $t = 0,$ their positions and direction of motion are shown in the figure:

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The relative velocity $\vec{V_{A}} - \vec{V_{B}}$ at $t = \frac{π}{2 ω}$ is given by:

A runner completes one round of a circular path of radius r in 40 seconds. His displacement after 2 minutes 20 seconds will be

Important Questions on Rotational Dynamics

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A runner completes one round of a circular path of radius $r$ in $40$ seconds. His displacement after $2$ minutes $20$ seconds will be