Rotation RETEACH. Main Topics to be Covered Circular Motion  Remember, uniform circular motion- constant velocity Conical Pendulum A ball of mass m.

Slides:



Advertisements
Similar presentations
Newton’s Laws Rotation Electrostatics Potpourri Magnetism
Advertisements

Chapter 8: Dynamics II: Motion in a Plane
Chapter 11 Angular Momentum
Warm-up: Centripetal Acceleration Practice
GRAVITATIONAL MOTION.
Physics 106: Mechanics Lecture 04
MSTC Physics Chapter 8 Sections 3 & 4.
Torque Torque and golden rule of mechanics Definition of torque r F
Physics 7C lecture 13 Rigid body rotation
Lecture 16: Rotational Motion. Questions of Yesterday 1) You are going through a vertical loop on roller coaster at a constant speed. At what point is.
Physics 101: Lecture 15, Pg 1 Physics 101: Lecture 15 Rolling Objects l Today’s lecture will cover Textbook Chapter Exam III.
Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.
Physics 111: Mechanics Lecture 10 Dale Gary NJIT Physics Department.
Chapter 11: Rolling Motion, Torque and Angular Momentum
Rotational Motion – Part II
Chapter 11 Rolling, Torque, and Angular Momentum In this chapter we will cover the following topics: -Rolling of circular objects and its relationship.
Physics 2 Chapter 10 problems Prepared by Vince Zaccone
Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 24, 25 Hw: Chapter 15 problems and exercises.
CIRCULAR MOTION We will be looking at a special case of kinematics and dynamics of objects in uniform circular motion (constant speed) Cars on a circular.
General Physics 1, Additional questions By/ T.A. Eleyan
5.2 Uniform Circular motion 5.3 Dynamic of Uniform Circular Motion
Physics 151: Lecture 22, Pg 1 Physics 151: Lecture 22 Today’s Agenda l Topics çEnergy and RotationsCh çIntro to Rolling MotionCh. 11.
Using Newton’s Laws: Friction, Circular Motion, Drag Forces
Classical Mechanics Review 4: Units 1-19
Newton’s Laws of Motion
Chapter 8 Rotational Motion
Rotation and angular momentum
AP Physics C I.E Circular Motion and Rotation. Centripetal force and centripetal acceleration.
Rotation about a fixed axis
Angular Momentum of a Particle
Chapter 11 Angular Momentum.
Uniform Circular Motion the motion of an object traveling in a circular path an object will not travel in a circular path naturally an object traveling.
Chapter 8: Torque and Angular Momentum
Lecture 21: REVIEW: PROBLEMS. Questions of Yesterday 1) Ball 1 is thrown vertically in the air with speed v. Ball 2 is thrown from the same position with.
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.
Dynamics II Motion in a Plane
Q10. Rotational Motion.
Rotational Dynamics Just as the description of rotary motion is analogous to translational motion, the causes of angular motion are analogous to the causes.
ROTATIONAL MOTION AND EQUILIBRIUM
Chapter 10 - Rotation Definitions: –Angular Displacement –Angular Speed and Velocity –Angular Acceleration –Relation to linear quantities Rolling Motion.
AP Physics B I.E Circular Motion and Rotation. I.E.1 Uniform Circular Motion.
Potential Energy and Conservative Forces
T071 Q17. A uniform ball, of mass M = kg and radius R = 0
Physics 201: Lecture 19, Pg 1 Lecture 19 Goals: Specify rolling motion (center of mass velocity to angular velocity Compare kinetic and rotational energies.
Chapter 8 Rotational Motion.
CHAPTER 6 : CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS
 Extension of Circular Motion & Newton’s Laws Chapter 6 Mrs. Warren Kings High School.
10. Rotational Motion Angular Velocity & Acceleration Torque
Physics 111 Practice Problem Statements 10 Torque, Energy, Rolling SJ 8th Ed.: Chap 10.6 – 10.9 Contents 11-47, 11-49*, 11-55*, 11-56, 11-60*, 11-63,
Uniform Circular Motion Centripetal forces keep these children moving in a circular path.
Work, Power and Energy in Rotational Motion AP Physics C Mrs. Coyle.
Rotational Motion. Angular Quantities Angular Displacement Angular Speed Angular Acceleration.
Copyright © 2009 Pearson Education, Inc. Chapter 5 Using Newton’s Laws: Friction, Circular Motion, Drag Forces.
Torque. So far we have analyzed translational motion in terms of its angular quantities. But we have really only focused on the kinematics and energy.
Uniform Circular Motion the motion of an object traveling in a circular path an object will not travel in a circular path naturally an object traveling.
Rotational Motion. 6-1 Angular Position, Velocity, & Acceleration.
ROTATIONAL MOTION Y. Edi Gunanto.
9 Rotation Rotational Kinematics: Angular Velocity and Angular Acceleration Rotational Kinetic Energy Calculating the Moment of Inertia Newton’s Second.
Chapter 11 Angular Momentum. The Vector Product and Torque The torque vector lies in a direction perpendicular to the plane formed by the position vector.
Short Version : 10. Rotational Motion Angular Velocity & Acceleration (Instantaneous) angular velocity Average angular velocity  = angular displacement.
Rotational Inertia & Kinetic Energy AP Phys 1. Linear & Angular LinearAngular Displacementxθ Velocityv  Accelerationa  InertiamI KE½ mv 2 ½ I  2 N2F.
Chapter 8 Rotational Kinematics – Angular displacement, velocity, acceleration © 2014 Pearson Education, Inc. Info in red font is not necessary to copy.
 Gravity is 9.8 or ~10 m/s 2  If dropped from rest: y = -½ gt 2.
Chapter 5:Using Newton’s Laws: Friction, Circular Motion, Drag Forces
Chapter 5:Using Newton’s Laws: Friction, Circular Motion, Drag Forces
Rotational Motion AP Physics.
Chapter 11 Angular Momentum
Rotational Kinetic Energy
Rotational Kinetic Energy
Chapter 5:Using Newton’s Laws: Friction, Circular Motion, Drag Forces
Presentation transcript:

Rotation RETEACH

Main Topics to be Covered

Circular Motion  Remember, uniform circular motion- constant velocity Conical Pendulum A ball of mass m is suspended by a string of length L. The ball revolves with a constant speed v in a horizontal circle of radius r. Determine the horizontal component of tension on the string. Vertical component of T. What is the total amount of tension on the string?

Tarzan Problem Tarzan (m = 85.0 kg) tries to cross a river by swinging from a vine. The vine is 10.5 m long, and his speed at the bottom of the swing (as he just clears the water) is 9.00 m/s. Tarzan doesn't know that the vine has a breaking strength of 1000 N. Find the tension on the vine. Does Tarzan make is across the river?

Riding a Ferris Wheel A child of mass m rides a Ferris wheel. The child moves in a vertical circle of radius 10 m at a constant speed of 3 m/s.  Determine the force exerted by the seat on the child at the bottom of the ride in terms of mg.  Determine the force exerted by the seat on the child at the top of the ride in terms of mg

Rotational Kinematic Equations (all for constant alpha) For any motion given as a function of time

Angular Acceleration The angular speed of an automobile engine is increased from 1200 rev/min to 3000 rev/min in 12s. What is the acceleration in rev/min^2, assuming it to be uniform?

Position Function

Spinning Baseball A good pitcher can throw a baseball at 85 mph with a spin of 1800 rev/min. How many revolutions does the baseball make on its way to home plate if it is 60ft away (and the trajectory is a straight line)?

Unwinding String A pulley wheel 8.0cm in diameter has a 5.6 m long cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of 1.5 rad/s^2.  Through what angle must the wheel for the cord to unwind?  How long does it take?

Net Acceleration A car starts from rest and moves around a circular track of radius 30.0m. Its speed increases at the constant rate of m/s^2. What is the magnitude if its net linear acceleration 15 s later?

Rotational Kinetic Energy

Flywheel

Rolling Up a Ramp A solid 8kg sphere rolls up an incline with an inclination of 30 degrees. At the bottom of the incline the center of mass of the sphere has a translational speed of 9.3 m/s.  What is the kinetic energy of the sphere at the bottom of the incline?  How far does the sphere travel up the incline?  If it was a 10kg ball would the height be: less than, greater, or equal to the previous answer?

Rolling with a Loop A small solid marble of mass m and radius r rolls without slipping along the loop the loop track, having been released from rest. The radius of the loop-the-loop track is R with R >>> r  From what minimum height h above the bottom of the track must the marble be released in order that it not leave the track at the top of the loop?

Torque Basics C B D A EF  Torque is produced No torque is produced

Direction of Torque r F θ θ Right-Hand Rule: Shows direction of torque  cross-product r Fsinθ  magnitude + Counter clockwise - clockwise

Net Torque

Difficulty Tightening a Bolt C B A

So what about pulleys? In AP 1 you used pulley systems… BUT ignored mass and size of pulley ( essentially ignoring moment of inertia of pulley itself)

Mass-less Pulley (unrealistic system) A gram mass ( m 1 ) and 50.0-gram mass ( m 2 ) are connected by a string. The string is stretched over a pulley.  Determine the acceleration of the masses and the tension in the string.

Another Mass-less pulley Consider the two-body situation at the right. A 20.0-gram hanging mass (m 2 ) is attached to a gram air track glider (m 1 ).  Determine the acceleration of the system and the tension in the string.

Why are these solutions not correct & impossible??

So what about pulleys? We’ve ignored mass and size of pulley ( moment of inertia of pulley itself) BUT… THE PULLEY IS ROTATING Why is this a crucial piece of information in the system?

Net Torque

Analyzing Tension ALONG Pulleys  If the tension is the same for both sides of the string, what is the Net Torque? T T rr If torque is the tendency to rotate, we know the pulley is rotating, but we calculate 0 N m net torque, is this feasible?

Newton’s Second Law of Rotation

The original solution is wrong because we ignored this rotating pulley. Analyzing Tension ALONG Pulleys T r T T T

Realistic Pulley System A gram mass ( m 1 ) and 50.0-gram mass ( m 2 ) are connected by a string. The string is stretched over a pulley. The pulley is 75 grams and 10cm in diameter.  Determine the acceleration of the masses and the tension in each side of the string.

Another Realistic Pulley System Consider the two-body situation at the right. A 20.0-gram hanging mass (m 2 ) is attached to a gram air track glider (m 1 ).  Determine the acceleration of the system and the tension in the string.

Rolling Down a Ramp A uniform sphere rolls down an incline.  What must be the incline angle if the linear acceleration of the center of the sphere is 0.10g?  For this angle, what would be the acceleration of a frictionless block sliding down the incline?