MEDIUM

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A disk shaped coin is tossed up in the air with 'Head' side on the top. The initial centre of mass velocity of the coin is $6.8 m \cdot s^{- 1}$ in the vertical direction. In addition, the disk is rotating about the horizontal axis with angular velocity $6 π rad \cdot s^{- 1}$ . Assume the motion in air is torque-free. Find the number of completed flips the disk will perform before it hits the ground under the action of gravity.

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Important Questions on Motion

HARD

Science>Physics>Motion>Angular Variables

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?

HARD

Science>Physics>Motion>Angular Variables

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:

EASY

Science>Physics>Motion>Angular Variables

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,

EASY

Science>Physics>Motion>Angular Variables

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

Science>Physics>Motion>Angular Variables

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)

EASY

Science>Physics>Motion>Angular Variables

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

HARD

Science>Physics>Motion>Angular Variables

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:

MEDIUM

Science>Physics>Motion>Angular Variables

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

EASY

Science>Physics>Motion>Angular Variables

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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EASY

Science>Physics>Motion>Angular Variables

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,

EASY

Science>Physics>Motion>Angular Variables

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

360 rpm

1200 rpm

14 s

. Its angular acceleration is,

MEDIUM

Science>Physics>Motion>Angular Variables

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

Science>Physics>Motion>Angular Variables

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

EASY

Science>Physics>Motion>Angular Variables

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:

MEDIUM

Science>Physics>Motion>Angular Variables

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

Science>Physics>Motion>Angular Variables

If a point charge

q

is moving in a circle of radius

r

with speed

v,

then time period

T

of the point charge will be

HARD

Science>Physics>Motion>Angular Variables

Two blocks of masses $m$ and $2 m$ connected by a massless string move along concentric horizontal circles on a horizontal frictionless table with $O$ as fixed point as shown in the figure. If $T$ is the period of motion, the tension in the longer part of the string is (Neglect the dimensions of the blocks when compared with the lengths of the string).

Question Image

EASY

Science>Physics>Motion>Angular Variables

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

EASY

Science>Physics>Motion>Angular Variables

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

EASY

Science>Physics>Motion>Angular Variables

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:

Question Image

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

Important Questions on Motion

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