More Related Content
Viewers also liked
Recently uploaded
Recently uploaded (20)
7
- 2. F ˆ F www.schoolDD.com 1 F vcmF F 7 - F F F F F F F F F F F ˈ F 7.1 F F 1. ીሬሬറ F ˈ ˈ F F ˈ (rad) 2. ሬሬሬറ F F ˈ F F ˈ / (rad/s) 3. F હሬሬറ F ˈ F F ˈ / 2 (rad/s2 ) cm. ω ω ω + cm. sr θ θ = ܛ ܚ ࣓ሬሬሬറ = ીሬሬറ ܜ θ = ଶగ୰ ୰ = 2ߨ t = T F ω = ଶగ ࢻሬሬറ = ઢሬሬሬറ ઢܜ ωሬሬറθሬറ ω θ cm.
- 3. F ˆ F www.schoolDD.com 2 u ω F ( F ) F ˈ - F ω ω = ୲ F F F α = ன ୲ ¬ , F F α ˈ F 7.2 F F (v), (ω), F F (at) F (α) 1. F (v) (ω) 2. F F (at) F (α ) u = F F F v = F F ω0 = F ω = t = F F α = ன ୲ = ன ି னబ ୲ = ୴/୰ – ୳/୰ ୲ = ሺ ୴ – ୳ ୲ ሻ 1 r = at/r at = α r at = F F F v F ωr ω v = ω r v = ଶగ୰ ω = ଶగ F v = ω r v ω0 θ at = α rr
- 4. F ˆ F www.schoolDD.com 3 + v, at α ω t F F F F F F ˈ F F F ( F F F F ) F F s (m) θ (rad) F u (m/s) F ω0 (rad/s) v (m/s) ω (rad/s) F a (m/s2 ) F α (rad/s2 ) F F ( ) ( ) 1. v = u + at 1. ω = ω0 + αt 2. s = ሺ ୳ ା ୴ ଶ ሻ t 2. θ = ሺ னబ ା ன ଶ ሻ t 3. s = ut + ½ at2 3. θ = ω0t + ½ αt2 4. v2 = u2 + 2as 4. ω 2 = ω0 2 + 2αθ 5. s = v t ( v ) 5. θ = ω t ( ω ) F 1 ʽ F F 5 F 4/ ߨ / . 5 . F . . ʽ F 5 a t vu s ω0 θ ω
- 5. F ˆ F www.schoolDD.com 4 . ω = ? f = 4/ ߨ ω = ଶ = 2ߨf = 2ߨ(4/ ߨ) ω = 8 rad/s Ans . α = ? ω = ω0 + αt 8 = 0 + α(5) α = 1.6 rad/s2 Ans . θ = ? θ = ሺ னబ ା ன ଶ ሻ t = ሺ ା ଼ ଶ ሻ 5 θ = 20 rad Ans . = ? F . θ = 20 rad 1 F θ = 2ߨ rad θ = 20 rad F F 20/2ߨ = 3.18 Ans F 2 ˆˉ F 44 m 10 F F 70 cm F . F 10 . F F F F v= ?, a = ? ω0 = 0 t= 10 44 u= 0 ω ω0 = 0 f = 4/ߨ r= 0.70 ω = ?, α = ?
- 6. F ˆ F www.schoolDD.com 5 . ω = ?, v = ? t = 10 θ = ሺ னబ ା ன ଶ ሻ t ----1 θ F F 44 m F F F F 1 F F F = 2ߨr = 2(22/7)(0.70) = 4.4 m. F ˈ 44/4.4 = 10 F F 1 F θ = 2ߨ rad θ = 10 x θ = 10(2ߨ) = 20ߨ rad F θ = 20ߨ, ω0 = 0, t = 10 1, 20ߨ = ሺ ା ன ଶ ሻ 10 ω = 4ߨ rad/s Ans v = ωr = 4ߨ(0.7) v = 2.8ߨ m/s Ans . α = ?, a = ? ω = ω0 + αt 4ߨ = 0 + α(10) α = 0.4ߨ rad/s2 Ans a = α r = 0.4ߨ(0.7) a = 0.28ߨ m/s2 Ans 7.3 F F ࣎ F ˈ F F F ˈ (N m) m F ߬റ r ࣎ = F r F = mat at = αr F ߬ = mαr (r) = mr2 α ࣎ = I α I = mr2 = F
- 7. F ˆ F www.schoolDD.com 6 r3 F I ˈ F ˈ F F ˈ 2 (kg m2 ) ¬ F I F F F F F F 3 20 N F 2 kg 0.5 m F F F ˈ 4 F I F = ½ mr2 . F . F F F . F 4 . F F . ߬ = ? ߬ = Fr = 20(0.5) ߬ = 10 N m Ans . α = ?, at = ? ߬ = I α L A A m2 m3 m1 r3 r1r2 IA = ∑ ܚܕ IB = IA + ሺ∑ ܕሻ L2 L = B B = m1r1 2 + m2r2 2 + m3r3 2 = IA + (m1+ m2+ m3) L2 ω F = 20 + r = 0.5
- 8. F ˆ F www.schoolDD.com 7 = (½ mr2 ) α 10 = (½ x 2 x 0.52 ) α α = 40 rad/s2 Ans at = α r = 40(0.5) at = 20 m/s2 Ans . ω = ?, v = ? t = 4 s ω = ω0 + αt = 0 + 40(4) ω = 160 rad/s Ans v = ωr = 160(0.5) v = 80 m/s Ans . = ? F t = 4 s, θ = ሺ னబ ା ன ଶ ሻ t = ሺ ା ଵ ଶ ሻ 4 = 320 rad 1 F θ = 2ߨ rad θ = 320 rad F F 320/2ߨ = 50.8 Ans F 4 1 kg 2 kg F F 4 kg 0.5 m F F F F F ( I F = ½ mr2 ) F F F T1 T2 m1 T2 T1 aa m2 + r = 0.5 1 kg 2 kg + r = 0.5 1 kg 2 kg m1g m2g F F T1 T2 F F F I F F a m1 m2 F m = 4
- 9. F ˆ F www.schoolDD.com 8 ߬ = F F r F ߬ = (T2- T1) r ߬ = I α F I α = (T2- T1) r ----1 m1 m2 ∑ F = ma F T1 m1g = m1a --> T1 = m1a + m1g m2g T2 = m2a --> T2 = m2g m2a T2 - T1 = (m2 - m1) g (m1 + m2) a F F T2 - T1 = (2 - 1) 10 (1 + 2) a T2 - T1 = 10 3 a F a = α r T2 - T1 = 10 - 3α r = 10 - 3α (0.5) T2 - T1 = 10 1.5 α ----2 F T2 - T1 I = ½ mr2 1 F ½ mr2 α = (10 1.5 α) r ½ (4)(0.52 ) α = (10 1.5 α) (0.5) α = 4 rad/s2 Ans a = α r = 4(0.5) a = 2 m/s2 Ans F α 2, T2 - T1 = 10 1.5 (4) T2 - T1 = 4 N ߬ = (T2- T1) r = 4 (0.5) ߬ = 2 N m Ans F 5 F F I = ½ mr2 r F F F F F F F F F a T + r F F
- 10. F ˆ F www.schoolDD.com 9 f F F F T ߬ = Tr ߬ = I α F T = I α/ r F F ∑ F = ma F mg T = ma F T = I α/ r a = αr F mg I α/ r = m αr mg ½ mr2 α/ r = m αr α = ଶ ଷ୰ ߬ = I α F ߬ = ½ mr2 ଶ ଷ୰ ߬ = ଵ ଷ mgr N m Ans F 6 m r F F F F F . F F F ( I = ଶ ହ mr2 ) F F F F ߬ = f r ߬ = I α F f = I α/ r ----1 ∑ F = ma F mg sin37 f = ma F f = I α/ r a = αr mg 37° 37° a mg cos37 mg sin37 mg N F F
- 11. F ˆ F www.schoolDD.com 10 F mg sin37 I α/ r = m αr mg sin37 ଶ ହ mr2 α/ r = m αr α = ହ ୱ୧୬ଷ ୰ F I α 1, f = ଶ ହ mr2 ( ହ ୱ୧୬ଷ ୰ ሻ/ r f = ଶ mg sin37 F f = µN = µ mg cos37 µ mg cos37 = ଶ mg sin37 µ = ଶ x ଷ ହ x ହ ସ = ଷ ଵସ µ = 0.21 Ans 7.4 F Ek 1. F 2. F ( ) F 7 20 kg 1 m F 5/π / F (I = mr2 ) v ω I + + EK = ½ I ω2 ω I + + EK = ½ mv2 + ½ I ω2 v ω I
- 12. F ˆ F www.schoolDD.com 11 F Ek = ½ mv2 + ½ Iω 2 ----1 F f = 5/π ω = 2π f = 2π (5/π ) = 10 rad/s v = ωr = 10(1) 10 m/s I = mr2 = 20(12 ) = 20 kg m2 F 1, Ek = ½ 20(102 ) + ½ 20(10 2 ) Ek = 2x103 J Ans F 8 (v) m r F h (I = ଶ ହ mr2 ) . v = ? ( F F f = 0) F ∑ Eଵ = ∑ Eଶ mgh = ½ mv2 v = ඥ2gh Ans . v = ? F ∑ Eଵ = ∑ Eଶ mgh = ½ mv2 + ½ Iω 2 mgh = ½ mv2 + ½ ଶ ହ mr2 ( ୴ ୰ ሻ 2 gh = ୴మ ଶ + ୴మ ହ v = ට ଵ୦ Ans F F u = 0 v h . F . F
- 13. F ˆ F www.schoolDD.com 12 7.5 W F P ˈ F ˈ F (w) F 9 F 72 km/hr F F F 0.5 m F 1x 104 kg - m2 F F F F F F F F v = 72 km/hr = 20 m/s ω = ୴ ୰ = ଶ .ହ = 40 rad/s ω2 = ω0 2 + 2αθ 402 = 0 + 2αθ αθ = 800 W = ߬ θ = Iαθ = 1x104 (800) W = 8x106 J Ans m F r W = ࣎ θθθθ W = Fs ߬ = Fr F W = ሺ ఛ ୰ ሻ s F ୱ ୰ = θ W = ߬ θ θ s P = ࣎ ω P = ୲ W = ߬ θ F P = ఛ ୲ F ୲ = ω P = ߬ ω u = 0 ω0 = 0 v = 20 ω r = 0.5, I = 1x104 F F
- 14. F ˆ F www.schoolDD.com 13 F 10 F F F 1000 N m F 120/π / F F P = ߬ ω = 1000(4) P = 4000 W Ans 7.6 L ߬ = I α = I ሺ ன ି னబ ୲ ሻ = ୍ன ି ୍னబ ୲ ߬ = ୲ F ∑ ۺ F = ∑ ۺ ω ߬ = 1000 ω = 2π f = 2π (120/(60 π )) ω = 4 rad/s I ω L = Iω ˈ F F ˈ kg m2 /s ࣎ = ઢۺ ઢܜ F =
- 15. F ˆ F www.schoolDD.com 14 I1ω1 = I2ω2 F 11 F 4 rad/s ( I = 2.5 kg m2 , I = 2.0 kg m2 ) F I1ω1 = I2ω2 2.5(4) = 2.0 ω2 ω2 = 5 rad/s Ans I F F F F F F F F ( s ) ⇔ (θ) F (v) ⇔ (ω) F F (a) ⇔ F (α) (m) ⇔ F ( I ) ( F) ⇔ F (߬ ) (p) ⇔ ( L) F F = ma F ߬ = I α p = mv L = I ω F = ୮ ୲ F ߬ = ୲ W = Fs W = ߬ θ P = Fv P = ߬ω F Ek = ½ mv2 F Ek = ½ I ω 2 I1 = 2.5 ω1 = 4 ω2 = ? I2 = 2.0
- 16. F ˆ F www.schoolDD.com 15