大物5 1剛體和基本運(yùn)動(dòng)

第5力矩繞定軸轉(zhuǎn)動(dòng)剛體的動(dòng)能

形狀和體積不變化——AA

:

2n 2nrBrA

rBrABr

rAn rAnAvAv aAx

y轉(zhuǎn)軸固定不動(dòng)—定軸轉(zhuǎn)動(dòng)

zIPIP

f

(運(yùn)動(dòng)學(xué)?程)

dfdd2

f當(dāng) 當(dāng)

0t

1t2

00

2(0v

v 2an 2advr

5.2力矩 矩 矩

1.1.F對(duì)z(?FMz(F)FrFMz(F)FrsinFhzFh AFnFOr MOr大小MOrFzFzFrA

F m Fk mk

fk

mkak

mkrkrk

F (m

kk kk 與?頓第?定律比較：MFJm,

MJΔmkJΔmk2kJrVr 確定轉(zhuǎn)動(dòng)慣量的三個(gè)要素:(1)總質(zhì)量 (2)質(zhì)量分布(3)轉(zhuǎn)軸的位置MLOxJLx2MLOx

Lx2

dx1 J鐵J mO O0J LR2dm00

2πR0R22πRdl2πR0

RRrmOdm

m2πrdr2mr J mr2dmR2mr3drmR2 MLOMLOxMLMLOxJLx2dx1

JL/2x2dx

1 /2 zMLC *L*r=20cm的飛輪邊緣，在繩端施以F=98N不計(jì)，(見(jiàn)圖)(1 r解 Fr Fr980.239.2 T(2)mgTTrJar

Jmr2980.510

21.8m1m2的物體掛于滑輪上，繩與滑輪間無(wú)相對(duì)滑動(dòng)。解以

，

m為研究對(duì)象,

物體m：mgTm Tmgm

物體

T1rT2rJ

2

1 m1

t

m

1

m

1 Δm1,Δm2,,Δmk,zOrkPr,r,zOrkP v,v,,v, Δmk 1Δm

21Δm

EEk

Δm

Δmk

22

22 2ωωOFrr'.Pr

A

M=

AM( A2Md2(M)d

2Md

dAMd(Jd)dJdd(1J2) A2dA

2

1

2

J2

mlxCmlxC解M12A

Md

l2lmgsin01J2

J1ml232l

lOrSPOOrSPOO rPrOLOrpsin

Lrp點(diǎn),此時(shí)m相對(duì)三個(gè)點(diǎn)的距離分別為d1、d2、d3 d

LB LCC

rF

rmvr

r

d(mv)dr

M

Mdt

2Mdt1

M0，則L

──質(zhì)點(diǎn)動(dòng)量矩守恒

守恒條件

0 FO O

LmvrsinmΔrrsin2m

M Mr例發(fā)射一宇宙飛船去 解引?場(chǎng)（有?? O1mv

GMm1mv2GMm

vrmv0r0sin(π) v 0 4vsin 3GM1/

3GM1/sin1

2

vv01

2 Z軸的動(dòng)量矩

Z mvrmrZZ Δmvr i

viLZ

Δmr2Ji LZ

對(duì)定軸轉(zhuǎn)動(dòng)剛體，Jz

JZ

M2MzdtdLz2

Mzd1

2dJ

（動(dòng)量矩定理積分形式Mz Lz 變形體繞某軸轉(zhuǎn)動(dòng)時(shí)，若Mz LzJkk kJtω常 mv0y N其中J 1ML2

mv01ML2my 3?速?轉(zhuǎn)的陀螺在陀螺重?對(duì)?點(diǎn)?速?轉(zhuǎn)的