Daily Handout Week 4 Day 1 Topics: Rotational Kinematics and Moment of Inertia Submit to Blackboard by 11:59 pm. Upload to W4D1-HO Folder 1. The angular position θ as a function of t of a reference line of a rotating disk is given by θ (t)=(0.25rads2)𝑡2+ (−0.85𝑟𝑎𝑑𝑠)𝑡 +(−2.3 𝑟𝑎𝑑) Calculate the angular acceleration as a function of time α(t)? Is the angular acceleration constant? Answer: α= 0.5 ra/s2 , yes. 2. When a fan is turned off, its angular speed decreases from 10 rad/s to 6.3 rad/s in 5.0 s. What is the magnitude of the average angular acceleration of the fan? Answer: α= 0.74 rad/s^2 3. An old LP record that is originally rotating at 33.3 rad/s is given a uniform angular acceleration of 2.15 rad/s2. Through what angle has the record turned when its angular speed reaches 72.0 rad/s? Answer: θ=948 rad 4. What is the angular speed, in rad/s, of a flywheel turning at 813.0 rpm? Answer: ω = 85.14 rad/s5. Two spheres have the same radius and equal masses. One is made of solid aluminum, and the other is made from a hollow shell of gold. Which one has the bigger moment of inertia about an axis through its center? 6. Two spheres have the same radius and equal mass. One is made of solid aluminum, and the other is made from a hollow shell of gold. The axis of rotation for the solid sphere is at the rim, and the axis of rotation for the hollow sphere is through the center. Which one has the bigger moment of inertia? 7. Consider a solid sphere of uniform density, total mass M and radius R that is rotating about the axis shown, which lies along its outer edge. What is the moment of inertia about this axis? Use parallel-axis theorem Answer: I = (7/5)MR2 8. Three balls, with masses of 3M, 2M, and M, are fastened to a massless rod of length L as shown. What is the moment of inertia aka rotational inertia about the left end of the rod? Answer: 32ML29. Consider a solid sphere of uniform density, total mass M and radius R that is rotating about the axis shown, which lies along its outer edge. What is the moment of inertia about this axis? Use parallel-axis theorem. Answer: 75MR2 10. What is the moment of inertia for a uniform beam of total mass M and length L that is pivoted around an axis of rotation that passes L/6 from the left end as, as shown? Use parallel-axis theorem or integration method Answer: 736ML211. Consider a uniform thin rod of length L and mass M rotated about an axis perpendicular to the rod and passing a point L/4 from left end. What is the moment of inertia of the rod about this point? Use parallel-axis theorem or integration method. I=7/48 ML^2 12. Consider a solid cylinder of uniform density, total mass M, and radius r that is rotating about the axis shown, which lies along its outer edge. What is the moment of inertia about this axis? Answer: I = 3/2 MR213. Consider a thin uniform rod of mass M and length L. The rod is rotated about an axis passing through the left end of the rod. Calculate the moment of inertia of the rod at this point using: (a) Parallel –axis theorem (b) Integration method Answer: I = 1/3 ML2 14. A truck of mass 500.0 kg moving to the right at 15.0 m/s crashes into a car of mass 250 kg moving to the left at a speed of 40.0 m/s. (a) Sketch before and after pictures assuming they stick together. (b) What is the initial momentum just before the crash? (c) What is the final momentum just after crash? (d) If the car and truck stuck together after the crash, how fast is the wreckage moving after collision and in which direction? (e) Compute the total kinetic energy before the crash. (f) Compute the total kinetic energy after the crash. (g) Is the mechanical energy conserved, and what type of collision does this answer imply? Answers: (a) Sketch (b) -2500 kg m/s (c) -2500 kg m/s (d) -3.33 m/s (e) 256000 J (f) 4160 J (g)