Mphindi ya inertia

1. Nthawi ya kusagwira ntchito bwino kwa tinthu tating'onoting'ono

Unikani tinthu tozungulira. Tinthu tomwe tili ndi kulemera kwa m timapatsidwa mphamvu ya F kuti tinthuto tizizungulira mozungulira mzere wa O. Tinthuto tili r kutali ndi mzere wozungulira. Choyamba, tinthuto timakhala pampando (v = 0). Tikasuntha ndi mphamvu ya F, tinthuto timayenda ndi liwiro linalake kuti tinthuto tizikhala ndi kuthamanga kwa tangential. Ubale pakati pa mphamvu (F), kulemera (m), ndi kuthamanga kwa tangential kwa tinthuto umafotokozedwa ndi equation 3:

F = ma _tan (Equation 3)

Tinthu timeneti timazungulira kotero kuti tinthu timeneti timakhala ndi kufulumira kwa angular. Ubale pakati pa kufulumira kwa tangential ndi kufulumira kwa angular ukufotokozedwa ndi equation 4:

a _tan = r α (Equation 4)

M'malo mwa a mu equation 3 ndi a mu equation 4:

F = mr α

r F = mr ² α

τ = (mr ² ) α (Chiyerekezo 5)

r F ndi mphindi ya mphamvu ndipo mr ² ndi mphindi ya inertia ya tinthu tating'onoting'ono. Equation 5 imafotokoza ubale pakati pa mphindi ya mphamvu, mphindi ya inertia, ndi angular acceleration ya tinthu tating'onoting'ono tozungulira. Equation 5 ndi equation ya lamulo lachiwiri la Newton la tinthu tating'onoting'ono tozungulira.

Nthawi ya inertia ya tinthu ndi zotsatira za kulemera kwa tinthu (m) ndi sikweya ya mtunda pakati pa tinthu tomwe tili ndi mzere wozungulira (r2 ⁾.

Ine = mr ² (Equation 6)

I = mphindi ya inertia ya tinthu, m = kulemera kwa tinthu, r = mtunda pakati pa tinthu ndi mzere wozungulira. Equation 6 imagwiritsidwa ntchito kudziwa mphindi ya inertia ya tinthu.

3.2 Zitsanzo za mavuto a nthawi ya inertia ya tinthu tating'onoting'ono

Chitsanzo cha vuto 1.

Tinthu tolemera makilogalamu awiri tinamangiriridwa ku chingwe cha mamita 0.5 m'litali kenako n’kuzunguliridwa. Kodi nthawi ya kulephera kwa tinthu timeneti ikazungulira ndi yotani?

yankho;

Ine = Bambo ²

I = (2 kg) (0.5 m) ²

I = 0.5 kg m ²

Chitsanzo cha vuto 2.

Tinthu tiwiri, chilichonse chokhala ndi kulemera kwa 2 kg ndi 4 kg, timalumikizidwa ndi waya wopepuka, pomwe kutalika kwa waya ndi mamita awiri. Musanyalanyaze kulemera kwa mawaya. Dziwani nthawi yomwe tinthu tiwiri timeneti timalephera kugwira ntchito, ngati:

a) Mzere wozungulira uli pakati pa tinthu tiwiri

yankho;

Ine = m ₁ r ₁ ² + m ₂ r ₂ ²

Ine = (2)(12) + (4)(12)

Ine = 2 + 4

I = 6 kg m ²

b) Mzere wozungulira uli pamtunda wa mamita 0.5 kuchokera pa tinthu tolemera makilogalamu 2

Ine = m ₁ r ₁ ² + m ₂ r ₂ ²

Ine = (2)(0.5 ² ) + (4)(1.5 ² )

Ine = (2)(0.25) + (4)(2.25)

Ine = 0.5 + 9

I = 9.5 kg m ²

c) Mzere wozungulira uli pamtunda wa mamita 0.5 kuchokera pa tinthu tolemera makilogalamu 4

Ine = m ₁ r ₁ ² + m ₂ r ₂ ²

Ine = (2)(1.52) + (4)(0.5 ² )

Ine = (2)(2.25) + (4)(0.25)

Ine = 4.5 + 1

I = 5.5 kg m ²

Kutengera ndi zotsatira za mawerengedwe omwe ali pamwambapa, nthawi ya inertia imakhudzidwa kwambiri ndi malo a mzere wozungulira. Ngakhale mawonekedwe ndi kukula kwake ndizofanana chifukwa malo a mzere wozungulira ndi osiyana, nthawi ya inertia nayonso ndi yosiyana.

Tinthu tating'onoting'ono tomwe tili pafupi ndi mzere wozungulira timakhala ndi nthawi yochepa ya inertia, pomwe tinthu tating'onoting'ono tomwe tili kutali ndi mzere wozungulira timakhala ndi nthawi yayikulu ya inertia. Ngati tiganiza kuti tinthu tating'onoting'ono timene tili pamwambapa ndi zinthu zolimba, ndiye kuti tinthu tating'onoting'ono tonse tili pafupi ndi mzere wozungulira.

Ili ndi mphindi yochepa ya inertia kuposa mphindi ya inertia ya tinthu tating'onoting'ono tomwe tili kutali ndi mzere wozungulira.

3.3 Nthawi ya kusakhazikika kwa thupi lolimba lofanana

Zinthu zolimba zimapangidwa ndi tinthu tambirimbiri. Nthawi ya kusakhala ndi mphamvu kwa thupi lolimba ndi chiwerengero chonse cha nthawi ya kusakhala ndi mphamvu kwa tinthu tating'onoting'ono tomwe timapanga chinthucho.

Ine = Σ mr ²

Ine = m₁ r₁² +m₂ r₂² +m₃ r₃² + ….. + m_n r_n²

Kuti tidziwe nthawi ya inertia ya chinthu cholimba, tiyenera kuwunikanso chinthucho pamene chikuzungulira chifukwa malo a mzere wozungulira amakhudza nthawi ya inertia ya chinthucho. Nthawi ya inertia (I) ya tinthu tonse imadaliranso kulemera (m) kwa tinthu ndi sikweya ya mtunda (r ² ) wa tinthu kuchokera ku mzere wozungulira. Kulemera kwa tinthu tonse tomwe timamanga chinthucho ndi kulemera kwa chinthucho.

Vuto ndilakuti, mtunda wa tinthu tating'onoting'ono tomwe timazungulira umasiyana.

Unikani kuchepa kwa fomula ya mphindi ya inertia ya mphete yopyapyala yokhala ndi zala R ndi kulemera M.

Ngati mzere wozungulira uli pakati pa mphete, tinthu tonse ta mphete yopyapyala timapezeka kuchokera ku mzere wozungulira. Nthawi ya inertia ya mphete yopyapyala imafanana ndi nthawi ya inertia ya tinthu tonse:

Ine = Σ mr²

Ine = m₁ r₁² +m₂ r₂² +m₃ r₃² + ….. + m_n r_n²

Kulemera kwa tinthu tonse = kulemera kwa mphete yopyapyala (M)

Ine = M (r ₁ ² + r ₂ ² + r ₃ ² + ….. + r _n ² )

Tinthu tating'onoting'ono ta mphete yopyapyala ndi r kuchokera ku mzere wozungulira kotero kuti r ₁ = r ₂ = r ₃ = rn = R

Kuyerekeza kwa mphindi ya inertia ya mphete yopyapyala:

Ine = MR ²

I = mphindi ya kulephera kwa mphete yopyapyala, M = kulemera kwa mphete yopyapyala, R = utali wa mphete yopyapyala.

Nanga bwanji ngati mzere wozungulira suli pakati pa mphete? Ngati mzere wozungulira suli pakati pa mphete, njira ya mphindi ya inertia ya mphete yopyapyala singapezeke pogwiritsa ntchito njira yomwe ili pamwambapa,

chifukwa mtunda wa tinthu tating'onoting'ono kuchokera ku mzere wozungulira ndi wosiyana. Kupeza njira ya nthawi ya inertia ya vuto ngati ili sikukambidwa pankhaniyi.

Fomula ya mphindi ya inertia ya zinthu zina zolimba

3.4 Chitsanzo cha vuto la nthawi ya kutopa kwa thupi lolimba lofanana

Chitsanzo cha vuto 1:

Silinda ya ndodo AB imakhala ndi kulemera kwa makilogalamu atatu ikazunguliridwa kudzera mu B,

mphindi ya kulephera ndi 27 kg m ^2. Kodi mphindi ya kulephera ndi chiyani ngati

yazunguliridwa kudzera mu C?

yankho;

yankho;

Fomula ya mphindi ya inertia ya ndodo yolimba yofanana (mzere wozungulira uli pakati pa ndodo):

I = 1/12 ML ²

27 = (1/12) ML ²

(27)(12) = ML ²

324 = ML ²

Fomula ya mphindi ya inertia ya ndodo yolimba yofanana (mzere wozungulira m'mphepete mwa ndodo):

I = 1/3 ML ²

Ine = 1/3 (324)

I = 108 kg m ²