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Address 15. Snippet of Idleness Rotational Active Vitality Precise Energy. Inactivity and Increasing speed. Direct Rotating. Power Torque. Change in movement . Balance: strengths (torques) are in parity ( = zero). Progress: powers (torques) are non zero. Impact. Cause.
Transcripts
Slide 1

﻿Address 15 Moment of Inertia Rotational Kinetic Energy Angular Momentum Physics 103, Spring 2004, U. Wisconsin

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Inertia and Acceleration Linear Rotary Force Torque Change in movement Equilibrium: strengths (torques) are in adjust ( = zero) Dynamics: powers (torques) are non zero Effect Cause How is torque identified with rakish speeding up? What is what might as well be called mass? How would we express Newton\'s law for rotational movement? Material science 103, Spring 2004, U. Wisconsin

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Moment of Inertia When an inflexible protest is liable to a net torque ( ≠0), it experiences a rakish speeding up Where the compel is connected on the body matters Distribution of mass about the body matters The precise increasing speed is specifically corresponding to the net torque The relationship ∑ t = I an is comparable to ∑F = mama Newton\'s Second Law The precise quickening is conversely corresponding to the snapshot of dormancy, I, of the question Mass of a bit of the question (m i ) Distance from pivot of turn to that piece (r i ). SI units are kg-m 2 Physics 103, Spring 2004, U. Wisconsin

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Moment of Inertia of a Uniform Ring Image the circle is separated into various little fragments, m 1 … These sections are equidistant from the pivot Physics 103, Spring 2004, U. Wisconsin

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Preflight 14.4 The rotational latency of an unbending body: is a measure of its imperviousness to changes in rotational movement. relies on upon the area of the pivot of revolution. is huge if the majority of the body\'s mass is a long way from the hub of turn. is the greater part of the above is nothing from what was just mentioned Physics 103, Spring 2004, U. Wisconsin

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Preflight 14.5 & 14.6 A band, a strong barrel and a strong circle all have a similar mass and sweep. Which of them has the biggest snapshot of dormancy when they pivot about hub appeared? The loop. The barrel. The circle All have a similar snapshot of dormancy Physics 103, Spring 2004, U. Wisconsin

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Preflight 14.7 & 14.8 The photo beneath shows two diverse dumbbell molded items. Question A has two wads of mass m isolated by a separation 2L, and protest B has two bundles of mass 2m isolated by a separation L. Which of the articles has the biggest snapshot of idleness for pivots around x-hub? A. B. They have a similar snapshot of dormancy Physics 103, Spring 2004, U. Wisconsin

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Moments of Inertia Physics 103, Spring 2004, U. Wisconsin

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Question M Imagine hitting a dumbbell with a protest coming in at speed v, first at the inside, then toward one side. Is the focal point of-mass speed of the dumbbell the same in both cases? 1. Yes. 2. No Case 1 Case 2 The moving article comes in with a specific energy. In the event that it hits the middle, as in the event that 1 , there is no turn, and this impact is much the same as a one dimensional crash between protest of mass m and another of mass 2m. Due to the bigger mass of dumbbell, the approaching ball skips back. In the event that 2, the dumbbell, begins turning. The approaching ball experiences less "resistance" and in this manner exchanges less of its energy to the dumbbell , which will along these lines have a littler focus of-mass speed than in the event that 1. Material science 103, Spring 2004, U. Wisconsin

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Rotational Kinetic Energy Work must be done to pivot objects Force used opposite to the range Parallel to the removal D s q r F Physics 103, Spring 2004, U. Wisconsin

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Rotation Summary (with correlation with 1-d direct movement) Angular Linear Physics 103, Spring 2004, U. Wisconsin

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Question CORRECT You choose to move two protests down a slope to see which one gets to the base first. Protest A will be a strong barrel and question B is an empty chamber. An and B have a similar mass and sweep. Assume you discharged them from rest at the highest point of the slope at same time, which one gets to the base of the incline first? 1. A 2. B 3. Same the snapshot of inactivity for a strong chamber is not as much as that of an empty barrel implying that more potential vitality can be changed over to translational dynamic vitality instead of rotational active vitality I w 2/2 ...this implies A will get to the base quicker in light of the fact that it will cover a more noteworthy separation for each unit time Physics 103, Spring 2004, U. Wisconsin

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Lecture 15, Preflight 4 & 5 CORRECT Two chambers of a similar size and mass move down a slope. Chamber A has the majority of its mass gathered at the edge, while barrel B has the greater part of its mass assembled at the middle. Which achieves the base of the slope first? 1. A 2. B 3. Both reach in the meantime. Barrel A has higher snapshot of latency than chamber B - in this way, it takes more time to move down. Material science 103, Spring 2004, U. Wisconsin

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Question CORRECT In the moving examination, which protest has the most active vitality when it gets to the base of the slope? 1. A 2. B 3. Same Gravity is in charge of movement. Protection of vitality reveals to us that PE will be transformed into KE. Both will have the same KE at the base, since they had a similar PE (mgh is same since they had a similar mass and shape, and began from a similar stature) at the highest point of the slope. The aggregate motor vitality is the total of translational (mv 2/2) and rotational (I w 2/2). What about speed in the wake of moving down a similar stature? Material science 103, Spring 2004, U. Wisconsin

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Speed of Sliding Object Physics 103, Spring 2004, U. Wisconsin

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Kinetic Energy w V CM Physics 103, Spring 2004, U. Wisconsin

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Kinetic Energy: Rolling without Slipping w V CM Physics 103, Spring 2004, U. Wisconsin

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Application: Rolling without Slipping Down Incline w V CM h KE add up to + PE g = 0 PE g = - Mgh Solve: Physics 103, Spring 2004, U. Wisconsin

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Application: Rolling without Slipping Down Incline w V CM h Larger I  littler V CM Physics 103, Spring 2004, U. Wisconsin

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Roller Coaster CORRECT Small Large Physics 103, Spring 2004, U. Wisconsin

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Angular Momentum Similarly to the connection amongst drive and energy in a straight framework, we can demonstrate the connection amongst torque and precise force Angular energy is characterized as L = I w and Physics 103, Spring 2004, U. Wisconsin

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Lecture 15, Preflight 1 CORRECT L w p q r The precise energy of a molecule is free of the particular starting point of directions. is zero when its position and force vectors are parallel. is zero when its position and force vectors are opposite. Rakish force, L = I w = ( S mr 2 ) (v/r) i.e., L = mv r = r p (here r and p make 90 o ) Angular energy is a vector opposite to the position, r, and movement, p , L = r x p Right hand control Physics 103, Spring 2004, U. Wisconsin

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Angular Momentum Physics 103, Spring 2004, U. Wisconsin

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Angular Velocity, Momentum - Right Hand Rule Physics 103, Spring 2004, U. Wisconsin

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Angular Momentum Conservation If the net torque is zero, the rakish energy stays consistent Conservation of Linear Momentum expresses: The precise force of a framework is monitored when the net outer torque following up on the frameworks is zero. That is, when Physics 103, Spring 2004, U. Wisconsin

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Angular Momentum Conservation Physics 103, Spring 2004, U. Wisconsin

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Lecture 15, Preflight 2 & 3 CORRECT A figure skater remains on one spot on the ice (expected frictionless) and twists around with her arms augmented. When she pulls in her arms, she diminishes her rotational idleness and her precise speed builds so that her rakish force is saved. Contrasted with her underlying rotational active vitality, her last rotational motor vitality after she has pulled in her arms must be: 1. Same 2. Bigger in light of the fact that she is turning quicker 3. Littler on the grounds that her rotational latency is littler Rotational active vitality is I w 2/2. L=I w . Rot.K.E=L w/2 L is steady - in this manner, since w expands Rot. KE additionally increments. Extra vitality is given by the skater "working" to force her arms in. Material science 103, Spring 2004, U. Wisconsin

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Lecture 15, Pre-flights You are perched on an unreservedly pivoting bar-stool with your arms extended and an overwhelming glass mug in each hand. Your companion gives you a curve and you begin turning around a vertical pivot however the focal point of the stool. You can accept that the bearing the stool turns on is frictionless, and that there is no net outside torque display once you have begun turning. You now pull your arms and hands (and mugs) near your body. Material science 103, Spring 2004, U. Wisconsin

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Lecture 15, Preflight 6 & 7 CORRECT L 1 L 2 What happens to your rakish force as you draw in your arms? 1. it builds 2. it diminishes 3. it remains the same Since there is no outer torque following up on the framework, the aggregate rakish energy is saved. Material science 103, Spring 2004, U. Wisconsin

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Lecture 15, Preflight 8 & 9 CORRECT w 2 w 1 I 2 I 1 L What happens to your rakish speed as you draw in your arms? 1. it expands 2. it diminishes 3. it remains the same Your snapshot of inactivity reductions so your rakish speed must increment to make up for this change and keep precise energy the same. Material science 103, Spring 2004, U. Wisconsin

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Lecture 21, Preflight 10 & 11 (utilizing L = I  ) CORRECT w 2 w 1 I 2 I 1 L What happens to your active vitality as you draw in your arms? 1. it expands 2. it diminishes 3. it remains the same Because w increments as much as I abatements. In the condition: KE decay = 1/2 I w 2 , w is squared so the motor vitality increments. You are doing work by changing your snapshot of latency so you increment your motor vitality Physics 103, Spring 2004, U. Wisconsin

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Question (utilizing L = I  ) Two distinctive turning plates have the same precise force , yet circle 2 has a bigger minute

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