Kinematics of Rotational Motion

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JEE Main 2021, 20 July Shift-II

LEVELJEE Main

A body rotating with an angular speed of $600 rpm$ is uniformly accelerated to $1800 rpm$ in $10 s$ . The number of rotations made in the process is …… .

LEVELJEE Advanced

A pulley of radius $2 m$ is rotated about its axis by a force $F = (20 t - 5 t^{2}) N$ (where, $t$ is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is $10 kg-m^{2}$ , then the number of rotations made by the pulley before its direction of motion is reserved, is

(A)

more than 3 but less than 6

(B)

more than 6 but less than 9

JEE Main 2021, 17 March Shift-I

LEVELJEE Main

The angular speed of truck wheel is increased from $900 rpm$ to $2460 rpm$ in $26 s$ . The number of revolutions by the truck engine during this time is ……… . (Assuming the acceleration to be uniform).

JEE Advanced 2012

LEVELJEE Advanced

Consider a disc rotating in the horizontal plane with a constant angular speed $ω$ about its centre $O$ . The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles $P$ and $Q$ are simultaneously projected at an angle towards $R$ . The velocity of projection is in the $y$ - $z$ plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed $1/8$ rotation, (ii) their range is less than half the disc radius, and (iii) $ω$ remains constant throughout. Then

(A)

P

lands in the shaded region and

Q

in the unshaded region

(B)

P

lands in the unshaded region and

Q

in the shaded region

(C)

both

P

and

Q

land in the unshaded region

(D)

both

P

and

Q

land in the shaded region

JEE Advanced 2017

LEVELJEE Advanced

A rigid uniform bar $A B$ of length $L$ is slipping from its vertical position on a frictionless floor (as shown in the figure). At some instant of time, the angle made by the bar with the vertical is $θ$ . Which of the following statements about its motion is/are correct?

* Multiple Correct Options

(A)

Instantaneous torque about the point in contact with the floor is proportional to

sin θ

(B)

The trajectory of the point

A

is parabola

(C)

The mid-point of the bar will fall vertically downward

(D)

When the bar makes an angle

θ

with the vertical, the displacement of its mid-point from the initial position is proportional to

(1 - cos θ)

JEE Advanced 2012

LEVELJEE Main

Comprehension Passage

The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass. These axes need not be stationary. Consider, for example, a thin uniform disc welded (rigidly fixed) horizontally at its rim to a massless stick, as shown in the figure. When the disc-stick system is rotated about the origin on a horizontal frictionless plane with angular speed

ω

, the motion at any instant can be taken as a combination of (i) a rotation of the centre of mass of the disc about the Z-axis, and (ii) a rotation of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the changed orientation of points

P

and

Q

). Both these motions have the same angular speed

ω

in this case. Now, consider two similar systems as shown in the figure : Case (a) the disc with its face vertical and parallel to x-z plane; Case (b) the disc with its face making an angle of

4 5^{\circ}

with x-y plane and its horizontal diameter parallel to X-axis. In both the cases, the disc is welded at point

P

, and the systems are rotated with constant angular speed

ω

about the Z-axis.

Question 1:

Which of the following statements regarding the angular speed about the instantaneous axis (passing through the centre of mass) is correct?

(A)

It is

2 ω

for both the cases

(B)

It is

ω

for case (a); and

\frac{ω}{2}

for case (b)

(C)

It is

ω

for case (a); and

2 ω

for case (b)

(D)

It is

ω

for both the cases

Question 2:

Which of the following statements about the instantaneous axis (passing through the centre of mass) is correct?

(A)

It is vertical for both the cases (a) and (b)

(B)

It is vertical for case (a); and is at

4 5^{\circ}

to the x-z plane and lies in the plane of the disc for case (b)

(C)

It is horizontal for case (a); and is at

4 5^{\circ}

to the x-z plane and is normal to the plane of the disc for case (b)

(D)

It is vertical for case (a); and is at

4 5^{\circ}

to the x-z plane and is normal to the plane of the disc for case (b)

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

An $L = 70 m$ long thin tape wound on a spool of radius $r_{0} = 10 mm$ makes a tape roll of outer radius $R = 25 mm$ . A motor used to wound the tape rotates the spool at a constant angular velocity and takes $T = 165 s$ to complete the winding. Calculate length of the tape, which has been wound in $t = 110 s$ from the beginning of the winding.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 s. The number of rotations made in the process is …… .

Comprehension Passage

Which of the following statements regarding the angular speed about the instantaneous axis (passing through the centre of mass) is correct?

Which of the following statements about the instantaneous axis (passing through the centre of mass) is correct?

A body rotating with an angular speed of $600 rpm$ is uniformly accelerated to $1800 rpm$ in $10 s$ . The number of rotations made in the process is …… .