1. Abu yana motsawa a cikin da'ira tare da saurin kusurwa mai 10 rad/s. Ƙayyade (a) Saurin kusurwa bayan daƙiƙa 10 (b) Saurin kusurwa bayan daƙiƙa 10.
An sani:
Gudun kusurwa (ω) = 10 rad/s
Ana so:
(a) Saurin kusurwa (ω) bayan daƙiƙa 10.
(b) Kusurwa (θ) bayan daƙiƙa 10
Magani:
(a) Saurin kusurwa (ω) bayan daƙiƙa 10
Abu a cikin motsi na zagaye iri ɗaya don gudun kusurwa ya kasance daidai, 10 rad/s.
(b) Matsar da kusurwa (θ)
Gudun kusurwa mai daidaito 10 radians/daƙiƙa yana nufin abu mai kusan radians 10 a kowace daƙiƙa. Bayan daƙiƙa 10, abu mai kusan radians 10 x 10 = radians 100.
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2. Ƙwayar cuta tana motsawa a cikin da'ira mai saurin mita 10/s. Radius na da'ira = mita 1. Ƙayyade (a) Gudun ƙwayar cuta bayan daƙiƙa 5 (b) Motsa ƙwayar cuta bayan daƙiƙa 5 (c) Hanzarta ta tsakiya.
An sani:
Radius na da'ira (r) = mita 1
Gudun barbashi (v) = 10 m/s
Magani:
(a) Saurin barbashi bayan daƙiƙa 5
Motsin abin yana cikin motsi mai zagaye iri ɗaya don haka gudun ya kasance mai daidaito, 10 m/s.
(b) Fitar da ƙwayoyin cuta bayan daƙiƙa 5
Mita 10/daƙiƙa yana nufin kowace daƙiƙa 1, ƙaurar ƙwayar cuta = mita 10. Bayan daƙiƙa 5, ƙaurar ƙwayar cuta = mita 5 x 10 = mita 50.
(c) Hanzarin tsakiya (a r )
a r = v 2 / r = 10 2 / 1 = 100 / 1 = 100 m/s 2
3. An juya ƙwallon da aka makala a ƙarshen igiya a cikin da'ira mai radius na mita 2 a gudun da ba ya canzawa na rpm 60. A ƙayyade (a) girman saurin kusurwa bayan daƙiƙa 2 (b) canjin kusurwa bayan minti 1.
An sani:
Radius na da'ira (r) = mita 2
Gudun kusurwa (ω) = 60 rpm = juyin juya hali 60 / minti 1
= Juyi 60 / daƙiƙa 60 = Juyi 1 / daƙiƙa = 2π radians / daƙiƙa
= 2(3.14) radians / daƙiƙa = 6.28 radians / daƙiƙa
Magani:
(a) Saurin kusurwa (ω) bayan daƙiƙa 2
Gudun kusurwar yana da daidaito don haka bayan daƙiƙa 2, saurin kusurwar (ω) = 6.28 radians / daƙiƙa
(b) Matsar da kusurwa (θ)
Saurin kusurwa = juyin juya hali 1/daƙiƙa yana nufin kowace daƙiƙa 1, ƙwallon tana fuskantar juyin juya hali 1. Bayan daƙiƙa 60, ƙwallon tana motsa juyin juya hali 60.
Gudun kusurwa = radians 6.28/daki yana nufin kowace dakika 1, ƙwallon yana motsawa da kusurwar radians 6.28. Bayan dakika 60, ƙwallon yana motsawa radians 376.8.
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4. Tayar keke tana juyawa sau 120 cikin daƙiƙa 60. Menene saurin kusurwa?
Magani:
(a) juyin juya hali a minti daya (rpm)
Juyin juya hali 120 / daƙiƙa 60 = juyi 120 / minti 1 = juyi 120 / minti = 120 rpm
(b) digiri a kowace daƙiƙa ( o / s)
Juyin juya hali 1 = 360 o , Juyin juya hali 120 = 43200 o
Juyawa 120 / daƙiƙa 60 = (120)(360 o ) / daƙiƙa 60 = 43200 o / daƙiƙa 60 = 720 o / daƙiƙa
(c) radians a kowace daƙiƙa (rad/s)
Juyin juya hali 1 = 6.28 radians
Juyawa 120 / daƙiƙa 60 = (120)(6.28) radians / daƙiƙa 60 = 753.6 radians / daƙiƙa 60 = 12.56 radians/daƙiƙa.
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