JEE Main Rotational Motion Practice Paper with Solutions and Answer Key

JEE Main Physics is one of the most important subjects for engineering aspirants, and it requires a thorough understanding of the fundamental concepts and principles. Rotational Motion  is a crucial topic in JEE Main Physics, and mastering this topic can help students score well in the exam. One of the best ways to prepare for JEE Main Physics is by solving practice papers on the Rotational Motion. In this article, we will discuss the importance of the JEE practice paper for Rotational Motion and Physics and how they can help students improve their problem-solving skills and test their knowledge of the concepts. These practice papers are available in various formats, including online and offline forms.

JEE Main Physics Practice Papers on Rotational Motion  - PDF Download

JEE Main Physics Practice Papers on Rotational Motion  PDF is a resource that provides a variety of questions on the topic, which can help students improve their problem-solving skills and develop a better understanding of the concepts. Here's what you can expect from JEE Main Physics Practice Papers on Rotational Motion in PDF format:

Types of Questions: JEE Main Physics Practice Papers on Rotational Motion cover a variety of questions, including multiple-choice questions, numerical-based questions, and assertion-reasoning questions. These questions are designed to test students' understanding of the concepts and principles of Rotational Motion.

Difficulty Level: JEE Main Physics Practice Papers on Rotational Motion  come with questions of varying difficulty levels. These practice papers have both easy and difficult questions, which can help students prepare for the exam and improve their problem-solving skills.

Detailed Rotational Motion: JEE Main Physics Practice Papers on Rotational Motion come with detailed Rotational Motion and answer keys. These Rotational Motion can help students understand the concepts better and identify their mistakes. The answer keys also help students evaluate their performance and identify areas to improve.

Vedantu's Physics Daily Practice Problems for JEE Main - Now with Rotational Motion!

Are you searching for a comprehensive and challenging set of Physics Rotational Motion practice problems to excel in your JEE Main preparation? Look no further than Vedantu's Physics Daily Practice Problems!

Our carefully selected problems cover all the important topics in the JEE Main Physics syllabus. We aim to provide you with a diverse range of problems that are challenging enough to enhance your problem-solving skills effectively.

To further support your learning, our problems are accompanied by detailed solutions. By analyzing these solutions, you can learn from your mistakes and deepen your understanding of the underlying concepts.

Why choose Vedantu's Physics Rotational Motion Daily Practice Problems?

Comprehensive coverage of the JEE Main syllabus: Our problems cover all the important topics in the Physics Rotational Motion JEE Main syllabus, ensuring you are well-prepared.

Challenging problems: Our problems are thoughtfully designed to challenge you and improve your problem-solving abilities, preparing you for the rigours of the JEE Main exam.

Detailed solutions: Each problem comes with detailed solutions, allowing you to identify your mistakes and gain clarity on the concepts involved.

Regular updates: We regularly update our problems to align with the latest JEE Main syllabus, ensuring you have access to the most relevant and up-to-date content.

How to make the most of Vedantu's Physics Rotational Motion Daily Practice Problems (DPPs):

Start with familiar topics: Begin by solving problems related to the Physics Rotational Motion topics you are already familiar with to build confidence.

Gradually tackle challenging problems: Once you have a strong foundation, gradually move on to more challenging problems to stretch your problem-solving abilities.

Seek help when needed: Don't hesitate to seek assistance if you encounter difficulties. Reach out to teachers or avail yourself of Vedantu's doubt-solving sessions to clarify your doubts and strengthen your understanding.

Review your solutions: Regularly review your solutions to identify areas of strength and weakness. This self-assessment will help you focus your efforts and improve your overall performance.

Stay updated: Stay abreast of the latest developments and changes in the JEE Main syllabus to ensure your preparation remains aligned with the exam requirements.

Sign up for Vedantu's Physics Daily Practice Problems today, now with the inclusion of the Rotational Motion chapter! Take advantage of our comprehensive set of practice problems to enhance your JEE Main preparation and increase your chances of success.

Start practicing with Vedantu's Physics Rotational Motion Daily Practice Problems and witness your progress soar!t

Topics of Rotational Motion

1. Center of a mass of a two-particle system: This practice paper delves into the concept of the center of mass in a two-particle system.

Understanding Center of Mass: The center of mass serves as the equilibrium point for a system comprising two particles. To pinpoint this center, the individual masses of the particles and their respective spatial positions are considered.

The center of mass is determined using the following formula:

Center of Mass $= \dfrac{(m_1 r_1 + m_2  r_2)}{(m_1 + m_2)}$

Here, 'm₁' and 'm₂' denote the masses of the two particles, while 'r₁' and 'r₂' represent their positions. Mastering this calculation is crucial for comprehending rotational motion, equilibrium, and stability in physical systems.

2. Center of the mass of rigid body; Basic concepts of a rotational motion; a moment of force; torque: This practice paper explores the fundamental concepts of the center of mass and torque in rotational motion.

Understanding the Center of Mass: The center of mass serves as the balance point for an entire object, signifying where it effectively balances. This calculation involves evaluating the distribution of mass within the object.

Delving into Rotational Motion: Rotational motion involves the spin and circular movement of objects. It's influenced by a twisting force called torque, calculated with the formula:

Torque (τ) = Force (F) $\times} Lever Arm (r) 

The lever arm is the perpendicular distance from the pivot point to the line of action of the force. Torque is pivotal in determining how objects rotate and balance, making it a core concept in the study of rotational motion.

3. Angular Momentum: Angular momentum depends on two critical factors: the moment of inertia (how mass is distributed in space) and angular velocity (how fast the object is spinning).

Formula for Angular Momentum: Angular Momentum (L) is calculated using the formula:

$L = I \times \omega$

where 'I' represents the moment of inertia and 'ω' is the angular velocity.

Significance of Angular Momentum: Understanding angular momentum helps us explain why objects continue to spin, cease their rotation, or alter their spin, making it a fundamental concept in the study of dynamic behavior in rotating systems.

4. Conservation of Angular Momentum and its applications: This practice paper dives into the law of conservation of angular momentum, similar to the conservation of linear momentum but specifically for rotating objects.

The Fundamental Principle: The conservation of angular momentum articulates that when external torques are absent, the total angular momentum of a system remains unaltered. In simpler terms, if a rotating object isn't subject to external twisting forces, its angular momentum remains constant.

Real-World Applications: This concept is widely applicable in various scenarios, such as understanding why ice skaters spin faster when they draw their limbs inward (reducing their moment of inertia) and elucidating the behavior of celestial bodies in space. Grasping the conservation of angular momentum empowers us to predict and explain the motion of rotating objects in diverse situations.

5. The moment of Inertia: This practice paper delves into the significance of moment of inertia, often considered the rotational analog of mass in linear motion.

Key Takeaways:

Moment of Inertia Defined: Moment of inertia, symbolized as 'I,' quantifies how an object's mass is distributed concerning its axis of rotation.

Illustrative Example: Visualize a figure skater executing graceful spins. As they draw their arms closer to their body, they spin faster. This effect occurs because their moment of inertia diminishes as mass is concentrated nearer to the axis of rotation.

Shape Matters: Moment of inertia is intrinsically connected to the object's shape and mass distribution. Mathematical formulas exist for simple shapes like rods or disks, facilitating its computation.

Crucial Predictive Tool: Comprehending moment of inertia is pivotal in foretelling how objects rotate, rendering it an essential concept in the realm of rotational motion studies.

6. The radius of gyration: The radius of gyration, symbolized as 'k,' offers a glimpse into how an object's mass is distributed concerning its axis of rotation.

Calculating k: This practice paper sheds light on the formula used to compute the radius of gyration: $k = \sqrt{\dfrac{I}{M}}$, where 'I' represents moment of inertia, and 'M' signifies the total mass.

Small vs. Large k: Understanding the radius of gyration helps distinguish between a small k (indicating concentrated mass near the rotation axis) and a large k (indicating mass spread out from the axis).

Simplifying Complex Rotational Calculations: This concept serves as a vital tool in streamlining intricate rotational calculations and is indispensable for comprehending how objects respond when they engage in spinning motion.

7. Values of moments of inertia for simple geometrical objects: Moments of inertia serve as the foundational blueprints for comprehending the rotational dynamics of different objects.

Calculating Moments of Inertia: This practice paper provides insights into how to calculate moments of inertia for specific shapes, such as a thin rod rotating about one end, a disk rotating around its central axis, and a hoop spinning around its central axis.

Empowering Predictions: Armed with these moment of inertia values, we can make accurate predictions about the behavior of objects as they engage in spinning motion.

Crucial for Rotational Analysis: Moments of inertia are essential tools in the study of rotational motion, offering a deeper understanding of how objects respond when subjected to rotation forces.

8. Parallel and perpendicular axes theorems: This practice paper delves into the powerful tools of parallel and perpendicular axes theorems, essential for calculating moments of inertia, especially for objects with intricate geometries.

1. Parallel Axes Theorem: Explore the parallel axes theorem's inner workings, which permit us to calculate the moment of inertia about an axis parallel to, but not through, the center of mass. This theorem simplifies the determination of moments of inertia for rolling objects and composite structures.

• Applications of Parallel Axes Theorem: Dive into real-world applications, including rolling objects like cylinders and spheres, where this theorem shines. Additionally, discover how to tackle the moment of inertia for composite objects with ease.

2. Perpendicular Axes Theorem: Unravel the mysteries of the perpendicular axes theorem, ideal for thin plates, disks, and composite objects with rotation occurring in two perpendicular directions. Learn to calculate moments of inertia when the plane of rotation is perpendicular to an object's thickness.

• Applications of Perpendicular Axes Theorem: See how this theorem aids in determining the moment of inertia for thin plates and composite structures, making complex geometries more manageable.

9. Rigid body rotation equation of rotational motion: Gain an in-depth understanding of the equation stating that the net torque acting on an object equals the rate of change of its angular momentum. Mathematically expressed as $\tau = \dfrac{dL}{dt}$, this equation is the cornerstone of rotational dynamics.

Applications and Insights: Explore how this equation plays a pivotal role in comprehending an object's angular motion under the influence of torques. Learn how it enables the prediction and analysis of rotational behavior, helping determine acceleration, deceleration, and the maintenance of constant angular velocity amidst various forces.

Important Formulas from Rotational Motion for JEE Main

1. Rotational Kinematics:

• Angular displacement: $\theta = \frac{s}{r}$

• Angular velocity: $\omega = \frac{\Delta \theta}{\Delta t}$

• Angular acceleration: $\alpha = \frac{\Delta \omega}{\Delta t}$

2. Rotational Dynamics:

• Moment of Inertia: $I = \sum m_i r_i^2$

• Torque: $\tau = I \cdot \alpha$

• Angular momentum: $L = I \cdot \omega$

• Rotational Work: $W = \tau \cdot \theta$

• Rotational Kinetic Energy: $KE = \frac{1}{2} I \omega^2$

3. Parallel-Axis Theorem: 

$I_{\text{new}} = I_{\text{CM}} + M \cdot d^2$

4. Rolling Motion: 

• Linear velocity of the center of mass: $v = R \cdot \omega$

• Angular velocity in terms of linear velocity: $\omega = \frac{v}{R}$

• Acceleration of the center of mass: $a = R \cdot \alpha$

• Rolling motion kinetic energy: $KE = \frac{1}{2} I \omega^2 + \frac{1/2} M v^2$

5. Angular Momentum Conservation:

• If no external torque acts on a system, the total angular momentum is conserved: $L_{\text{initial}} = L_{\text{final}}$