转动运动英文教材.pdf

Chapter 10 1 CHAPTER 10 - Rotational Motion About a Fixed Axis 1. (a) 30° = (30°)(π rad/180°) = π/6 rad = 0.524 rad; (b) 57° = (57°)(π rad/180°) = 19π/60 = 0.995 rad; (c) 90° = (90°)(π rad/180°) = π/2 = 1.571 rad; (d) 360° = (360°)(π rad/180°) = 2π = 6.283 rad; (e) 420° = (420°)(π rad/180°) = 7π/3 = 7.330 rad. 2. The subtended angle in radians is the size of the object divided by the distance to the object: θ = 2rSun/r; (0.5°)(π rad/180°) = 2r 6 5 Sun/(150 × 10 km), which gives rSun ≈ 6.5 × 10 km. 3. We find the distance from θ = h/r; 3 (7.5°)(π rad/180°) = (300 m)/r; which gives r = 2.3 × 10 m. 4. From the definition of angular acceleration, we have 2 α = Δω/Δt = [(20,000 rev/min)(2π rad/rev)/(60 s/min) – 0]/(5.0 min)(60 s/min) = 7.0 rad/s . 5. From the definition of angular velocity, we have ω = Δθ/Δt , and we use the time for each hand to turn through a complete circle, 2π rad. (a) ωsecond = Δθ/Δt = (2π rad)/(60 s) = 0.105 rad/s. (b) ωminute = Δθ/Δt –3 = (2π rad)/(60 min)(60 s/min) = 1.75 × 10 rad/s. (c) ωhour = Δθ/Δt –4 = (2π rad)/(12 h)(60 min/h)(60 s/min) = 1.45 × 10 rad/s. (d) For each case, the angular velocity is constant, so the angular acceleration is zero. 6. (a)