Chap5 - 8 Strategy Use the definition of average angular...

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8. Strategy Use the definition of average angular velocity. Solution In 1.0 s, the wheel rotates 2.0 rev 2 rad (1.0 s) 4.2 rad . 3.0 s rev t π θ ω ⎞⎛ Δ = Δ = = ⎟⎜ ⎠⎝ ω Δ θ 14. (a) Strategy and Solution The force of static friction between the inside wall of the rotor and the people’s backs keeps them from falling. (b) Strategy Use Newton’s second law and the relationship between angular speed and radial acceleration. Draw a free-body diagram. Solution 2 r r s and 0. y F N ma m r F f mg ω Σ = = = Σ = = Solve for . ω 2 2 s s s s 9.80 m s , so 3.1 rad s . 0.40(2.5 m) g f N m r mg r μ μ ω ω μ = = = = = = f N m g y s 19. (a) Strategy Use Newton’s second law and the relationship between radial acceleration and linear speed. Solution 2 r s r 0, so , and . y v F N mg N mg F f ma m R Σ = = = Σ = = = Find v . 2 s s s , so . v f mg m v gR R μ μ = = = (b) Strategy Consider the forces acting on the car. Solution Initially, the free-body diagram is N W f s
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