8.4. Newton’s Second Law for Rotational Motion

Slides:

Advertisements

Similar presentations

Angular Quantities Correspondence between linear and rotational quantities:

Advertisements

Rotational Equilibrium and Dynamics

Angular Momentum of a Point Particle and Fixed Axis Rotation 8.01 W11D1 Fall 2006.

Chapter 9 Rotational Dynamics.

L24-s1,8 Physics 114 – Lecture 24 §8.5 Rotational Dynamics Now the physics of rotation Using Newton’s 2 nd Law, with a = r α gives F = m a = m r α τ =

Chapter 9 Rotational Dynamics. 9.5 Rotational Work and Energy.

Ch 9. Rotational Dynamics In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of translation.

Physics Montwood High School R. Casao

Rotational Motion October 31, 2005 and November 2, 2005.

Class 28 - Rolling, Torque and Angular Momentum Chapter 11 - Friday October 29th Reading: pages 275 thru 281 (chapter 11) in HRW Read and understand the.

Chapter 11: Rolling Motion, Torque and Angular Momentum

Chapter 9 Rotational Dynamics.

Dynamics of Rotational Motion

2008 Physics 2111 Fundamentals of Physics Chapter 11 1 Fundamentals of Physics Chapter 12 Rolling, Torque & Angular Momentum 1.Rolling 2.The Kinetic Energy.

Rotational Dynamics Chapter 9.

Rolling 滾動, Torque and Angular momentum Rolling is a combination of translation of the center and rotation about the center. Since the rolling distance.

Vector- or Cross-product Torque Angular momentum Angular momentum is conserved!! Chapter 11: Angular Momentum Reading assignment: Chapter 11.1 to 11.4.

Chapter 5 Rotation of a Rigid Body. §5-5 Angular Momentum of a rigid Body Conservation of Angular Momentum §5-1 Motion of a Rigid body §5-2 Torque The.

Chapter 11: Angular Momentum

Chapter 12: Rolling, Torque and Angular Momentum.

Chapter 8 Rotational Equilibrium and Rotational Dynamics.

Physics 2211: Lecture 38 Rolling Motion

Physics 101: Lecture 18, Pg 1 Physics 101: Lecture 18 Rotational Dynamics l Today’s lecture will cover Textbook Sections : è Quick review of last.

Chapter Eight Rotational Dynamics Rotational Dynamics.

Physics 106: Mechanics Lecture 06 Wenda Cao NJIT Physics Department.

Torque and the vector product

Angular Momentum Lecturer: Professor Stephen T. Thornton

PH 201 Dr. Cecilia Vogel Lecture 20. REVIEW  Constant angular acceleration equations  Rotational Motion  torque OUTLINE  moment of inertia  angular.

Rotational Dynamics. Moment of Inertia The angular acceleration of a rotating rigid body is proportional to the net applied torque:  is inversely proportional.

Halliday/Resnick/Walker Fundamentals of Physics 8th edition

Angular Momentum Angular momentum of rigid bodies

Rotation and angular momentum

Angular Momentum of a Particle

-Angular Momentum of a Rigid Object -Conservation of Angular Momentum AP Physics C Mrs. Coyle.

Angular Momentum Definition: (for a particle)(for a system of particles) Units: compare with: Angular momentum and second Newton's law depends on the choice.

Chapter 8: Torque and Angular Momentum

Chapter 9 Rotations of Rigid Bodies Up to this point when studying the motion of objects we have made the (implicit) assumption that these are “point objects”

Chapters 10, 11 Rotation and angular momentum. Rotation of a rigid body We consider rotational motion of a rigid body about a fixed axis Rigid body rotates.

Rotation Rotational Variables Angular Vectors Linear and Angular Variables Rotational Kinetic Energy Rotational Inertia Parallel Axis Theorem Newton’s.

Rotational Dynamics and Static Equilibrium (Cont.)

Student is expected to understand the physics of rotating objects.

Chapter 9: Rotational Dynamics

Torque Chap 8 Units: m N 2.

Chapter 8 Rotational Motion.

Chapter 8 Rotational Motion.

Chapter 10 Chapter 10 Rotational motion Rotational motion Part 2 Part 2.

Rotational Mechanics. Rotary Motion Rotation about internal axis (spinning) Rate of rotation can be constant or variable Use angular variables to describe.

Rotational Dynamics Chapter 8 Section 3.

The center of gravity of an object is the point at which its weight can be considered to be located.

A car of mass 1000 kg moves with a speed of 60 m/s on a circular track of radius 110 m. What is the magnitude of its angular momentum (in kg·m 2 /s) relative.

9.4. Newton’s Second Law for Rotational Motion A model airplane on a guideline has a mass m and is flying on a circle of radius r (top view). A net tangential.

Moment Of Inertia.

Rolling motion (axis of rotation is moving) Torque Angular momentum Angular momentum is conserved Chapter 11: Angular Momentum part 2 Reading assignment:

Chapter 9 Rotational Dynamics.

Angular Momentum Section 8.1 (Ewen et al. 2005) Objectives: Define and calculate moment of inertia. Define and calculate moment of inertia. Define and.

Chapter 9 Rotational Dynamics

Rotational Dynamics 8.3. Newton’s Second Law of Rotation Net positive torque, counterclockwise acceleration. Net negative torque, clockwise acceleration.

Rolling, torque, and angular momentum

Cutnell/Johnson Physics 8th edition Reading Quiz Questions

Lecture 18: Angular Acceleration & Angular Momentum.

Rotational Dynamics The Action of Forces and Torques on Rigid Objects

Rotational Dynamics.

PHYSICS 111 Rotational Momentum and Conservation of Energy.

Year 13 Physics Rotation & Circular Motion. Rotation When either a rigid body or a particle rotates about some fixed point, we can describe the motion.

Rotational Motion.

Rotational Motion.

Rotational Dynamics Chapter 9.

Rotational Equilibrium and Dynamics

Rotational Kinematics

11.7 Angular Momentum Figure shows a particle of mass m with linear momentum as it passes through point A in an xy plane. The angular.

Presentation transcript:

8.4. Newton’s Second Law for Rotational Motion A model airplane on a guideline has a mass m and is flying on a circle of radius r (top view). A net tangential force FT acts on the plane. Newton’s 2nd law: F = ma What is the corresponding law?

NEWTON’S SECOND LAW FOR A RIGID BODY ROTATING ABOUT A FIXED AXIS

Moment of Inertia of point masses

Moment of Inertia, I for Extended regular- shaped objects

8.4 Rotational Work and Energy Work and energy are among the most fundamental and useful concepts in physics. The force F does work in rotating the wheel through the angle q.

ROTATIONAL WORK The rotational work WR done by a constant torque t in turning an object through an angle q is SI Unit of Rotational Work: joule (J) What does Wr correspond to???

ROTATIONAL WORK The rotational work WR done by a constant torque t in turning an object through an angle q is Linear: W = F d

ROTATIONAL KINETIC ENERGY What does this correspond to???

ROTATIONAL KINETIC ENERGY KE = ½ m v 2

Demo on Rolling Cylinders

8.5 Angular Momentum What does this correspond to??? The angular momentum L of a body rotating about a fixed axis is the product of the body's moment of inertia I and its angular velocity w with respect to that axis: SI Unit of Angular Momentum: kg · m2/s. What does this correspond to???

8.5 Angular Momentum Corresponds to p= m v Angular Momentum is the resistance to the change in rotation. The angular momentum L of a body rotating about a fixed axis is the product of the body's moment of inertia I and its angular velocity w with respect to that axis: SI Unit of Angular Momentum: kg · m2/s. Corresponds to p= m v

CONSERVATION OF ANGULAR MOMENTUM The total angular momentum of a system remains constant (is conserved) if the net external torque acting on the system is zero. L = always constant when no net torque is present. Note: I depends on Shape. When I drops, ω increases.

Demonstration on Conservation of angular momentum Chair Experiment http://www.exploratorium.edu/snacks/momentum_machine/

Problem A woman stands at the center of a platform. The woman and the platform rotate with an angular speed of 5.00 rad/s. Friction is negligible. Her arms are outstretched, and she is holding a dumbbell in each hand. In this position the total moment of inertia of the rotating system (platform, woman, and dumbbells) is 5.40 kg·m2. By pulling in her arms, she reduces the moment of inertia to 3.80 kg·m2. Find her new angular speed.