康涅狄格州大学：《普通物理》课程PPT教学课件（英文版）Lecture 11 Centripetal Acceleration

Physics 121, Sections 9, 10, 11, and 12 Lecture 11 Today's Topics Homework 5: Due Friday Oct 7@6: 00PM Ch.5:#9,11,12,23,26,30,32,41,57,and63. Chapter 5: Rotation Angular variables Centripetal acceleration Kepler's laws Artificial gravity Physics 121: Lecture 11, Pg 1

Physics 121: Lecture 11, Pg 1 Physics 121, Sections 9, 10, 11, and 12 Lecture 11 Today’s Topics: Homework 5: Due Friday Oct. 7 @ 6:00PM Ch.5: # 9, 11, 12, 23, 26, 30, 32, 41, 57, and 63. Chapter 5: Rotation Angular variables Centripetal acceleration Kepler’s laws Artificial gravity

Chapter 5 Uniform circular Motion What does it mean How do we describe it What can we learn about it Physics 121: Lecture 11, Pg 2

Physics 121: Lecture 11, Pg 2 Chapter 5 Uniform Circular Motion What does it mean ? How do we describe it ? What can we learn about it ?

Recap: X=R COS(0)=R coS(ot) y=R sin(0)=R sin(ot) 0= tan1 (y/x) R S 0= ot =0t s=vt S=R0 Rot V=OR Physics 121: Lecture 11, Pg 3

Physics 121: Lecture 11, Pg 3 Recap: R v s =t (x,y) x = R cos() = R cos(t) y = R sin() = R sin(t)  = tan-1 (y/x)  = t s = v t s = R = Rt v = R

Centripetal Acceleration UCM results in acceleration Magnitude a=v2/R =02R since v= OR Direction ( toward center of circle) Physics 121: Lecture 11, Pg 4

Physics 121: Lecture 11, Pg 4 Centripetal Acceleration UCM results in acceleration: Magnitude: a = v2 / R =  R since v = R Direction: - r (toward center of circle) R a  ^

Problem: Rotating puck weight A mass m, slides in a circular path with speed v on a horizontal frictionless table it is held at a radius r by a string threaded through a frictionless hole at the center of the table. At the other end of the string hangs a second mass m2 What is the tension in the string T? What is the speed of the sliding mass v Physics 121: Lecture 11, Pg 5

Physics 121: Lecture 11, Pg 5 Problem: Rotating puck & weight. A mass m1 slides in a circular path with speed v on a horizontal frictionless table. It is held at a radius R by a string threaded through a frictionless hole at the center of the table. At the other end of the string hangs a second mass m2 . What is the tension in the string T ? What is the speed of the sliding mass v ? m1 m2 v R

Problem: Rotating puck weight Draw FBD of hanging mass Since r is constant, a=0 SO T=m29 m29 Physics 121: Lecture 11, Pg 6

Physics 121: Lecture 11, Pg 6 Problem: Rotating puck & weight... Draw FBD of hanging mass: Since R is constant, a = 0. so T = m2g m2 m2g T m1 m2 v R T

Problem: Rotating puck weight N Draw Fbd of sliding mass: T=m29 m Use F=T=ma m,9 Where a=v2/R m m2g= m,V2/R g尺 m口 Physics 121: Lecture 11, Pg 7

Physics 121: Lecture 11, Pg 7 Problem: Rotating puck & weight... Draw FBD of sliding mass: m1 T = m2g v gR m m = 2 1 m1g N m1 m2 v R T Use F = T = m1a where a = v 2 / R m2g = m1v 2 / R

Forces Causing Centripetal Acceleration F=mac F mg Physics 121: Lecture 11, Pg 8

Physics 121: Lecture 11, Pg 8 Forces Causing Centripetal Acceleration r v a t c 2 = r v F ma t c 2 = = v F r mg m f n

Forces Causing Centripetal Acceleration Turn on a sloped road F=ma=-=n sin 0 n cos e 0 n sin e Physics 121: Lecture 11, Pg 9

Physics 121: Lecture 11, Pg 9 Forces Causing Centripetal Acceleration Turn on a sloped road …  mg n sin  2 n r v F ma t = c = = mg n sin  n cos 

Accelerated reference frames. The Accelerometer Your first job is with General Motors. You are working on a project to design an accelerometer The inner workings of this gadget consist of a weight of mass m that is hung inside a box that is attached to the ceiling of a car. You design the device with a very light string so that you can mathematically ignore it. The idea is that the angle the string makes with the vertical is determined by the cars acceleration. Your preliminary task is to think about calibration of the accelerometer. First you calibrate the measurement for when the car travels on a flat road Physics 121: Lecture 11, Pg 10

Physics 121: Lecture 11, Pg 10 Accelerated Reference Frames: The Accelerometer Your first job is with General Motors. You are working on a project to design an accelerometer. The inner workings of this gadget consist of a weight of mass m that is hung inside a box that is attached to the ceiling of a car. You design the device with a very light string so that you can mathematically ignore it. The idea is that the angle the string makes with the vertical is determined by the car’s acceleration. Your preliminary task is to think about calibration of the accelerometer. First you calibrate the measurement for when the car travels on a flat road