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Test: Angular Acceleration - JEE MCQ


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10 Questions MCQ Test Physics for JEE Main & Advanced - Test: Angular Acceleration

Test: Angular Acceleration for JEE 2024 is part of Physics for JEE Main & Advanced preparation. The Test: Angular Acceleration questions and answers have been prepared according to the JEE exam syllabus.The Test: Angular Acceleration MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Angular Acceleration below.
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Test: Angular Acceleration - Question 1

A particle moves in a circle of radius R with a constant speed. If its angular acceleration is doubled, how would the period of the particle's motion change?

Detailed Solution for Test: Angular Acceleration - Question 1

The period of a particle in circular motion is the time taken to complete one full revolution. The period is given by T = 2π/ω, where ω is the angular velocity. Angular acceleration, α, does not affect the period directly. The angular acceleration determines how quickly the angular velocity changes, but it does not affect the time taken for one complete revolution. Therefore, if the angular acceleration is doubled, the period of the particle's motion will remain the same.

Test: Angular Acceleration - Question 2

A wheel of moment of inertia 0.40 kg-m2 is making 2100 rotations per minute. The wheel is brought to a complete stop in 2 seconds. The angular acceleration of the wheel is

Detailed Solution for Test: Angular Acceleration - Question 2

CONCEPT:

  • Angular velocity (ω): How fast the angular position or orientation of an object changes with time or How fast an object rotates or revolves relative to another point is known as angular velocity.
    • Angular velocity in terms of RPM (revolutions per minute) 

ω = 2 π f / 60

where ω is in terms of radian per second and f is in revolution per minute.

  • Angular acceleration (α): The rate of change of angular velocity is known as angular acceleration.

The relation between α and changing ω is given by: 

ω1 = ω0 + α t

where ω1 is the final angular velocity, ω0 is the initial angular velocity α is the angular acceleration.

CALCULATION:

Given that f0 = 2100 rpm; f1 = 0 rpm; t = 2 sec.

ω0 = 2 π f0 / 60 = 2 π 2100 / 60 = 70π 

ω1 = 0

ω1 = ω0 + α t

0 = 70π + α 2

α = -35π rad/sec2

So the correct answer is option 1.

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Test: Angular Acceleration - Question 3

The angular acceleration is known as the rate of change of _________.

Detailed Solution for Test: Angular Acceleration - Question 3

CONCEPT:

  • Angular displacement (θ): The angular displacement of a body is the angle in degrees or radians or revolutions through which a point revolves around a point or axis.
  • Angular velocity (ω): How fast the angular position or orientation of an object changes with time or How fast an object rotates or revolves relative to another point is known as angular velocity.
    • It is the rate of change of angular displacement.​
  • Angular acceleration (α): The rate of change of angular velocity is known as angular acceleration.
  • Angular momentum (L): The moment of momentum is known as angular momentum.

CALCULATION:

  • The rate of change of angular velocity is known as angular acceleration. 

Mathematically,

α = dω/dt

  • So the correct answer is option 3.
Test: Angular Acceleration - Question 4

A circular disc is rotating about its own axis at uniform angular velocity ω. The disc is subjected to uniform angular retardation by which its angular velocity is decreased to ω/2​ during 120 rotations. The number of rotations further made by it before coming to rest is

Detailed Solution for Test: Angular Acceleration - Question 4

Test: Angular Acceleration - Question 5

A rod of length L fixed at the origin at one end is placed along the x-axis at t = 0. It starts rotating about the z-axis in the x-y plane anti-clockwise as seen from the positive z-axis. The angular displacement is given by θ = 2t2. The angular acceleration of the rod is

Detailed Solution for Test: Angular Acceleration - Question 5

Kinematic equations of rotational motion about a fixed axis,

where ω is the instantaneous angular velocity, α is the instantaneous angular acceleration, θ is the angular displacement, and t is time.

EXPLANATION:

Given: Length of the rod = L, and angular displacement θ = 2t2

  • Using the first equation,

  • Using the second equation, 


Therefore option 4 is correct.

Test: Angular Acceleration - Question 6

The moment of inertia of a particle of mass m kept at point (a, b) on the x-y plane about the x-axis is

Detailed Solution for Test: Angular Acceleration - Question 6

Moment of inertia:

  • Moment of inertia of a rigid body about a fixed axis is defined as the sum of the product of the masses of the particles constituting the body and the square of their respective distances from the axis of the rotation.
  • The moment of inertia of a particle  is

⇒ I = mr2

Where r = the perpendicular distance of the particle from the rotational axis.

  • Moment of inertia of a body made up of a number of particles (discrete distribution)

⇒ I = m1r12 + m2r22 + m3r32 + m4r42 + -------

EXPLANATION:

Given: mass of the particle = m, distance from x-axis = b.

The moment of inertia for the particle of mass m from an axis at a distance b is,

⇒ I = mb2

Therefore option 3 is correct.

Test: Angular Acceleration - Question 7

A wheel rotates with the constant acceleration of 2.0 rad/s2, if the wheel starts from rest the  number of revolution it makes in first ten seconds will be approximately 

Detailed Solution for Test: Angular Acceleration - Question 7

Test: Angular Acceleration - Question 8

Which of the following statements is correct about angular acceleration?

Detailed Solution for Test: Angular Acceleration - Question 8

Angular acceleration is defined as the rate at which an object's angular velocity changes over time. It is given by the formula:
Angular acceleration (α) = Change in angular velocity (Δω) / Change in time (Δt)

Test: Angular Acceleration - Question 9

A disc is rotating at 200 rad/s. If its angular acceleration is -10 rad/s², how long will it take for the disc to come to a complete stop?

Detailed Solution for Test: Angular Acceleration - Question 9

To find the time it takes for the disc to come to a complete stop, we can use the formula:
ω = ω + αt

where:
ω = final angular velocity (0 rad/s, as the disc comes to a complete stop),
ω = initial angular velocity (200 rad/s),
α = angular acceleration, and
t = time.

Rearranging the formula to solve for time (t):
t = (ω - ω) / α

Substituting the given values:
t = (0 - 200 rad/s) / (-10 rad/s²)
t = 20 seconds

Therefore, it will take 20 seconds for the disc to come to a complete stop.

Test: Angular Acceleration - Question 10

A wheel has an angular acceleration of 4 rad/s². If it starts from rest, how many revolutions will it complete in 10 seconds?

Detailed Solution for Test: Angular Acceleration - Question 10

The number of revolutions (N) completed by a wheel can be calculated using the formula:
N = (ωt + (1/2)αt²) 

where:
ω₀ = initial angular velocity (0 rad/s, as the wheel starts from rest),
t = time, and
α = angular acceleration.

Simplifying the formula for the given scenario:
N = (1/2)αt² 

Substituting the given values:
N = (1/2) * 4 rad/s² * (10 s)² 
N = 200 revolutions

Therefore, the wheel will complete 200 revolutions in 10 seconds.

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