# Fundamentals of Physics Chapter 11 Solutions: Rolling, Torque, and Angular Momentum

Halliday Resnick and Walker Fundamentals of Physics Volume 1 Solutions for Chapter 11 ‘Rolling, Torque, and Angular Momentum’ will help you revise all the concepts of the chapter for CBSE and JEE. This chapter of Resnick Halliday Solutions covers topics like forces and kinetic energy of rolling, working of a yo-yo, torque & its applications, angular momentum, newton’s second law in angular form, the angular momentum of a rigid body, conservation of angular momentum, the precession of a gyroscope, etc.

Physics Solutions for Resnick Halliday & Walker Fundamentals of Physics Extended Volume 1 Rolling, Torque, and Angular Momentum has 86 questions. All the questions have been divided into 10 modules that cover different topics of the chapter. After solving these questions, you will be able to attempt questions in your competitive exams like IIT JEE with great ease. You will be able to find the rotational kinetic energy, translational kinetic energy, linear speed, angular speed, inertia about a rotational axis, and frictional force acting on a unit area with the help of this chapter.

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## Important Topics for Resnick Halliday and Walker Fundamentals of Physics Volume 1 Solutions Chapter 11: Rolling, Torque, and Angular Momentum

**Rolling Bodies: **Rolling bodies function on the phenomena of rolling motion which is a combination of rotational and translational motion.

For a wheel of radius R rolling smoothly, its linear speed at its centre is given by the formula:

v_{com}= ωR

Here, com is the centre of mass, ω is the angular speed

The rolling wheel with mass M possess kinetic energy which is given by the formula:

K = ½ I_{com}2 + ½ M v_{com}^{2}

Here, I_{com} is the rotational inertia of the wheel at its center of mass, v_{com} is the linear speed at its center of mass

When the wheel with radius R is being accelerated, the acceleration of the center of mass is given by the formula:

a_{com}= αR

α is the angular acceleration

**Torque: **It is a type of force that causes a turning effect. It is a vector quantity. Torque is denoted by and is given by:

Where F is the force applied to a particle and r is a position vector locating the particle relative to the fixed point.

You can find the magnitude of torque by :

τ =r F sinφ

Here,φ is the angle between r and F

**Angular Momentum of a Particle: **You can calculate angular momentum L of a particle with mass m, linear velocity v, linear momentum p, and radius r by using the formula:

L = r x p = m(r x v)

And the magnitude can be calculated by using the formula:

L = r m v sinφ

Here,φ is the angle between r and p

**Newton’s Second Law in Angular Form: **You can use Newton’s second law for a particle in angular form as:

Here, L is the angular momentum of the particle and τ is the net torque acting on the particle.

**Angular Momentum of a Rigid Body: **You can calculate the Angular Momentum of a Rigid Body L by multiplying moment of inertia I and the angular velocity ω :

L = I x ω

**Conservation of Angular Momentum: **In an isolated system, when there is no torque acting, the angular momentum of a system remains constant.

So, L_{i} = L_{f}

i is the initial value and f is the final value

### Exercise Discussion of Resnick Halliday & Walker Fundamentals of Physics Volume 1 Solutions Chapter 11: Rolling, Torque, and Angular Momentum

**Module 1: Rolling as Translation and Rotation Combined**

This module contains 2 questions which are based on the concept of rolling. You are asked to find the angular velocity at different positions, distance, and angular acceleration.

**Module 2: Forces and Kinetic Energy of Rolling**

This module has 14 questions based on the concept of forces and energy possessed during rolling. The questions assess your understanding of rotational kinetic energy, rotational inertia, angular velocity, etc.

**Module 3: The Yo-Yo **

You will find only 2 questions on the topic of Yo-Yo. The questions ask you to calculate angular speed, linear speed, rotational kinetic energy, translational kinetic energy, tension, etc of a yo-yo.

**Module 4: Torque Revisited**

This module has 7 questions that test your knowledge on torque. You are asked to find the magnitude and direction of torque, angular velocity, acceleration, etc in unit vector notation.

**Module 5: Angular Momentum**

Here, you will come across 7 questions based on angular momentum. You are required to calculate the magnitude and direction of angular momentum, torque, the angle between velocity and force, etc.

**Module 6: Newton’s Second Law in Angular Form**

This module of Halliday Resnick and Walker Physics book contains 4 questions that assess your understanding of Newton’s Second Law in Angular Form. The questions ask you to calculate angular momentum, torque and derive expression of torque, etc.

**Module 7: Angular Momentum of a Rigid Body **

In this module, you will find 7 questions. The questions primarily ask you to calculate the angular momentum of a rigid body. Some questions are about calculating rotational inertia, angular velocity, work done on a wheel, etc.

**Module 8: Conservation of Angular Momentum**

This module contains 25 questions based on the concept of conservation of angular momentum. You will find some questions that ask you to find the ratio of the kinetic energy of the system, angle, angular speed, initial value of kinetic energy, the fraction of the rotational inertia, etc.

**Module 9: Precession of a Gyroscope**

You will find only 2 questions in this module that are based on the concept of Precession of a Gyroscope. The questions ask you to calculate the precession rate and direction of the precession

**Module 10: Additional questions **

This module contains 16 questions that cover all the concepts provided in the chapter such as rolling, angular velocity, angular acceleration, angular momentum, conservation of angular momentum, torque, rotational force, and rotational inertia, etc.

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