Momentum principle The change in momentum of a body is equal to the net force acting on the body times (乘) the duration of the interaction.

Slides:



Advertisements
Similar presentations
Angular Quantities Correspondence between linear and rotational quantities:
Advertisements

Chapter 11 Angular Momentum
Physics 106: Mechanics Lecture 04
Chapter 9 Rotational Dynamics.
Physics 7C lecture 13 Rigid body rotation
Rotational Equilibrium and Rotational Dynamics
Physics 111: Mechanics Lecture 10 Dale Gary NJIT Physics Department.
Rotational Equilibrium and Rotational Dynamics
Chapter 11: Rolling Motion, Torque and Angular Momentum
Dynamics of Rotational Motion
Angular Momentum (of a particle) O The angular momentum of a particle, about the reference point O, is defined as the vector product of the position, relative.
Chapter 11 Angular Momentum.
2008 Physics 2111 Fundamentals of Physics Chapter 11 1 Fundamentals of Physics Chapter 12 Rolling, Torque & Angular Momentum 1.Rolling 2.The Kinetic Energy.
Warm Up Ch. 9 & 10 1.What is the relationship between period and frequency? (define and include formulas) 2.If an object rotates at 0.5 Hz. What is the.
Rotational Dynamics Chapter 9.
Chapter 11 Angular Momentum.
Dynamics of a Rigid Body
Chapter 12: Rolling, Torque and Angular Momentum.
Chapter 10: Rotation. Rotational Variables Radian Measure Angular Displacement Angular Velocity Angular Acceleration.
Chapter 11 Rolling, Torque, and Angular Momentum In this chapter we will cover the following topics: -Rolling of circular objects and its relationship.
Reading Quiz A particle is located in the xy-plane at a location x = 1 and y = 1 and is moving parallel to the +y axis. A force is exerted on the particle.
Chapter 8 Rotational Equilibrium and Rotational Dynamics.
Chapter 11 Angular Momentum.
 Torque: the ability of a force to cause a body to rotate about a particular axis.  Torque is also written as: Fl = Flsin = F l  Torque= force x.
Chapter 11 Angular Momentum. The Vector Product There are instances where the product of two vectors is another vector Earlier we saw where the product.
Rotation Rotational Variables Angular Vectors Linear and Angular Variables Rotational Kinetic Energy Rotational Inertia Parallel Axis Theorem Newton’s.
Chapter 9: Rotational Dynamics
Chapter 10 - Rotation Definitions: –Angular Displacement –Angular Speed and Velocity –Angular Acceleration –Relation to linear quantities Rolling Motion.
Torque Chap 8 Units: m N 2.
Objectives  Describe torque and the factors that determine it.  Calculate net torque.  Calculate the moment of inertia.
Chapter 8 Rotational Motion.
Rotational Mechanics. Rotary Motion Rotation about internal axis (spinning) Rate of rotation can be constant or variable Use angular variables to describe.
Chapter 11 Rotational Mechanics. Recall: If you want an object to move, you apply a FORCE.
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.
Chapter 11 Angular Momentum. Angular momentum plays a key role in rotational dynamics. There is a principle of conservation of angular momentum.  In.
8.2 Rotational Dynamics How do you get a ruler to spin on the end of a pencil? Apply a force perpendicular to the ruler. The ruler is the lever arm How.
Physics CHAPTER 8 ROTATIONAL MOTION. The Radian  The radian is a unit of angular measure  The radian can be defined as the arc length s along a circle.
1 Rotation of a Rigid Body Readings: Chapter How can we characterize the acceleration during rotation? - translational acceleration and - angular.
AP Physics C Montwood High School R. Casao. When a wheel moves along a straight track, the center of the wheel moves forward in pure translation. A point.
Section 10.6: Torque.
Chapter 9 Rotational Dynamics
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.
Pgs Chapter 8 Rotational Equilibrium and Dynamics.
UNIT 6 Rotational Motion & Angular Momentum Rotational Dynamics, Inertia and Newton’s 2 nd Law for Rotation.
F1 F2 If F1 = F2… …no change in motion (by Newton’s 1st Law)
Goals for Chapter 10 To learn what is meant by torque
Causes of Rotation Sum the Torques.
Angular Momentum 7.2.
General Physics I Rotational Motion
Chapter 11: Rolling Motion, Torque and Angular Momentum
A pulley of radius R1 and rotational inertia I1 is
Rotational Inertia and Torque
Torque.
Rotational Dynamics Chapter 9.
Aim: How do we apply Newton’s 2nd Law of Rotational Motion?
Chapter 10: Rotational Motional About a Fixed Axis
Rolling, Torque, and Angular Momentum
Chapter 16. Kinetics of Rigid Bodies: Forces And Accelerations
Newton’s 2nd Law for Rotation
Rotational Dynamics Torque and Angular Acceleration
10.8   Torque Torque is a turning or twisting action on a body about a rotation axis due to a force, . Magnitude of the torque is given by the product.
Chapter 8 Rotational Motion.
Spring 2002 Lecture #15 Dr. Jaehoon Yu Mid-term Results
Chapter 11 - Rotational Dynamics
Chapter 11 Angular Momentum
Rotational Dynamics.
Dynamics of Rotational Motion
ROTATIONAL INERTIA AND THE ROTATIONAL SECOND LAW
Rigid body rotating around a point A
Presentation transcript:

Momentum principle The change in momentum of a body is equal to the net force acting on the body times (乘) the duration of the interaction.

Angular momentum principle The change in angular momentum of a body (around a given point) is equal to the net torque acting on the body (around the same point) times (乘) the duration of the interaction.

Angular momentum principle Greek letter “tau” Instantaneous version: where is the torque (力矩) around the point A.

Newton’s 2nd Law for rotation of a rigid body A (this step assumes the body is planar or symmetrical) Total torque due to external forces.

Example: A lever (杠杆) + A

Example: A lever (杠杆) + A Newton’s 2nd law:

Example: A lever (杠杆) + A If the lever is balanced, α = 0, so:

Example: A yo-yo (溜溜球) A yo-yo (assumed to be a cylinder) has mass M and radius R. Find its downward acceleration, and the tension force in the string Ft.

Homework: In a ‘real’ yo-yo, the string is wrapped around an axle with radius r < R. What is the advantage of this design? HINT: Assume the moment of inertia is the same as for a cylinder of radius R. How does the torque change?

Example: A bowling ball, rolling down a ramp Momentum principle, x direction:

Example: A bowling ball, rolling down a ramp Angular momentum principle, around center of mass (vectors along z axis): Substitute into momentum equation Compare to sliding.