Angular velocity thiab linear velocity - teeb meem thiab kev daws teeb meem

1. Ib lub pob nyob rau ntawm qhov kawg ntawm ib txoj hlua tig ib yam nkaus hauv ib lub voj voog kab rov tav ntawm lub voj voog radius 2 meters ntawm qhov ceev ntawm lub kaum sab xis tas li 10 rad/s. Txheeb xyuas qhov loj ntawm qhov ceev ntawm kab ncaj ntawm ib qho chaw nyob:

(a) 0.5 meters ntawm qhov chaw nruab nrab

(b) 1 meter ntawm qhov chaw nruab nrab

(c) 2 meters ntawm qhov chaw nruab nrab

Paub:

Lub vojvoog (r) = 0.5 meters s, 1 meters, 3 meters

Qhov ceev ntawm lub kaum sab xis = 10 radians s / se cond

Xav tau: linear velocity

Tshuaj:

v = r ω

v = qhov ceev ntawm kab , r = radius , ω = qhov ceev ntawm lub kaum sab xis

(a) Qhov ceev linear (v) ntawm ib qho chaw nyob ntawm r = 0.5 meters

v = r ω = (0.5 meters s )(10 rad/s) = 5 meters s /se cond

(b) Qhov ceev linear (v) ntawm ib qho chaw nyob ntawm r = 1 meter

v = r ω = (1 meter)(10 rad/s) = 10 meters s /se cond

(c) Qhov ceev linear (v) ntawm ib qho chaw nyob ntawm r = 2 meters s

v = r ω = (2 meters s )(10 rad/s) = 20 meters s /se cond

2. Cov hniav hauv lub tshuab sib tov tig ntawm tus nqi ntawm 5000 rpm. Txheeb xyuas qhov loj ntawm qhov ceev linear:

(a) ib qho chaw nyob 5 cm ntawm qhov chaw nruab nrab

(b) ib qho chaw nyob 10 cm ntawm qhov chaw nruab nrab

Paub:

Lub vojvoog (r) = 5 cm thiab 10 cm

Qhov ceev ntawm lub kaum sab xis (ω) = 5000 kho sawv daws / 60 vib nas thisob peb = 83.3 kho sawv daws / semob = (83.3)(6.28 radians) / semob = 523.3 radians / semob

Xav tau: Qhov loj ntawm qhov ceev linear

Tshuaj:

(a) Qhov loj ntawm qhov ceev ntawm ib qho chaw nyob 0.05 m ntawm qhov chaw nruab nrab

v = r ω = (0.05 m)( 523.3 rad/s) = 26 m/s

(b) Qhov loj ntawm qhov ceev ntawm ib qho chaw nyob 0,1 m ntawm qhov chaw nruab nrab

v = r ω = (0.1 m)( 523.3 rad/s) = 52 m/s

3. Ib lub taw tes ntawm ntug ntawm lub log uas muaj 30 cm hauv lub vojvoog, ncig ib lub voj voog ntawm qhov ceev tas li 10 meters/ib pliag.

Qhov loj ntawm qhov ceev ntawm lub kaum sab xis yog dab tsi?

Paub:

Lub vojvoog ( r) = 30 cm = 0.3 meters s

Qhov ceev linear (v) = 10 meters s / se cond

Xav tau: qhov ceev ntawm lub kaum sab xis

Tshuaj:

ω = v / r = 10 / 0.3 = 33 radians s /se cond

4. Lub tsheb uas muaj log tsheb loj li 50 cm, khiav tau 10 meters hauv 1 vib nas this. Lub kaum sab xis ceev npaum li cas?

Paub:

Lub vojvoog (r) = 0.25 meters

Qhov ceev ntawm ib qho taw tes ntawm ntug ntawm lub log tsheb (v) = 10 meters s / se cond

Xav tau: Qhov ceev ntawm lub kaum sab xis

Tshuaj:

ω = v / r = 10 / 0.25 = 40 radians s /se cond

5. Lub kaum sab xis ntawm lub log 20 cm hauv radians yog 120 rpm. Yog tias lub tsheb mus ncig hauv 10 vib nas this, qhov deb yog dab tsi.

Paub:

Lub vojvoog (r) = 20 cm = 0.2 meter s

Qhov ceev ntawm lub kaum sab xis = 120 rev / 60 setej yam kev mob = 2 rev / semob = (2)(6.28) radians / semob = 12.56 radians / semob

Xav tau: qhov deb

Tshuaj:

Qhov ceev ntawm ntug ntawm lub log:

v = r ω = (0.2 meter s )(12.56 radians s /se cond ) = 2.5 meters s /se cond

2.5 'meter's / second txhais tau tias yog ib qho chaw nyob ntawm ntug ntawm lub log mus ncig 2.5 'meter's txhua 1 vib nas this. Tom qab 10tej yam kev mob, lub ntsiab lus mus ncig 25 'meter's.

Yog li ntawd, qhov deb yog 25 meters.

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1. Kev hloov pauv cov chav ntawm lub kaum sab xis piv txwv cov teeb meem nrog cov kev daws teeb meem
2. Cov teeb meem thiab kev daws teeb meem ntawm cov qauv angular displacement thiab linear displacement
3. Cov teeb meem piv txwv ntawm angular velocity thiab linear velocity nrog cov kev daws teeb meem
4. Cov teeb meem piv txwv ntawm kev nrawm nrawm thiab kev nrawm nrawm linear nrog cov kev daws teeb meem
5. Cov teeb meem piv txwv ntawm kev txav mus los sib npaug nrog cov kev daws teeb meem
6. Cov teeb meem ntawm cov qauv centripetal acceleration nrog cov kev daws teeb meem
7. Cov teeb meem piv txwv ntawm kev txav mus los tsis sib xws nrog cov kev daws teeb meem