Hloov cov chav ntawm lub kaum sab xis (degree, radian, revolution)
1. ¼ rev = ….. o ( degree ) ?
tshuaj
1 lub voj voog = 360 o
½ rev = 180 o
¼ tig = 90 o
2. ½ rev = ……. r ad?
tshuaj
1 rev = 2 π rad = 2(3.14) rad = 6.28 rad
½ rev = pi rad = 3.14 rad
3. 180 o = ….. rev ?
tshuaj
360 o = 1 lub voj voog
180 o = ½ rev
[irp]
4. 90 o = ….. rad ?
tshuaj
360 AWG = 2.28 BTC
180 o = π rad = 3.14 rad
90 o = ½ π rad = ½ (3.14) = 1.57
5. 60 rad = ….. rev?
tshuaj
6.28 rad = 1 rev
60 rad/6.28 = 9.55 rev
6. 40 rad= ….. o?
tshuaj
6.28 rad = 360 o
40 rad/6.28 = (6.37)(360 o ) = 2292.99 o
[irp]
Kev hloov pauv ntawm lub kaum sab xis thiab kev hloov pauv ntawm txoj kab ncaj
1. Lub log tsheb kauj vab uas muaj txoj kab uas hla 60 cm tig tau 10 radians. Qhov kev hloov pauv ntawm ib qho ntawm ntug ntawm lub log yog dab tsi?
Paub:
Lub vojvoog (r) = 30 cm = 0.3 m
Lub kaum sab xis (θ ) = 10 radians
Xav tau: linear displacement (l)
Tshuaj:
l = rθ
l = (0.3 m)(10 rad)
l = 3 meters
2. Lub log uas muaj 50 cm radius tig tau 360 o . Qhov kev hloov chaw ntawm ib qho taw tes ntawm ntug ntawm lub log yog dab tsi?
Paub:
Lub vojvoog (r) = 50 cm = 0.5 meters
Lub kaum sab xis ( θ ) = 360 o = 6.28 radians
Xav tau: linear displacement (l)
Tshuaj:
l = rθ
l = (0.5 m)(6.28 rad)
l = 3.14 meters
[irp]
3. Lub log uas muaj lub vojvoog 50 cm tig tau 2 zaug. Qhov kev hloov pauv ntawm ib qho chaw ntawm ntug ntawm lub log yog dab tsi?
Paub:
Lub vojvoog (r) = 50 cm = 0,5 m
Lub kaum sab xis ( θ ) = 2 lub voj voog = (2)(6.28 radians) = 12.56 radians
Xav tau: linear displacement (l)?
Tshuaj:
l = rθ
l = (0.5 m)(12.56 rad)
l = 6.28 m
4. Ib qho chaw ntawm ntug ntawm lub log uas muaj 2 meters hauv lub vojvoog, txav mus 100 meters. Txheeb xyuas qhov kev hloov pauv ntawm lub kaum sab xis.
Paub:
Lub vojvoog (r) = ½ (txoj kab uas hla) = ½ (2 meters) = 1 'meter'
Kev hloov pauv kab ncaj (l) = 100 meters
Tshuaj:
(a) Kev hloov pauv ntawm lub kaum sab xis (hauv radians)
θ = s / r = 100 / 1 = 100 radians
(b) Kev hloov pauv ntawm lub kaum sab xis (hauv degrees)
1 radian = 360 o
100 radians = 100(360 o ) = 36,000 radians
(c) Kev hloov pauv ntawm lub kaum sab xis (hauv kev tig ib ncig)
6.28 radians = 1 revolution
36,000 / 6.28 = 5732,484 lub voj voog
[irp]
5. Ib lub khoom me me puag ncig ib lub voj voog 10 meters thiab tig 180 o . Lub radius yog dab tsi?
Paub:
Kev hloov pauv kab (l) = 10 meters
Lub kaum sab xis ( θ ) = 180 o = 3.14 radians
Xav tau: radius (r)
Tshuaj:
r = l / θ = 10 / 3.14 = 3.18 m
[irp]
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