Hw 4 Solutions - MPhys 2101 Homework 4 Solution Fall `06...

This preview shows page 1 - 3 out of 8 pages.

Phys 2101 Homework 4 Solution Fall `06 The numerical answers to the problems are calculated with the values used in the problems found in the printed textbook; the values for your particular WebAssign assignment will be different. 1. CQ.10-09. We have three flat disks, with the same size (same inner circle radius R c and the same outer shell radius R s ), the same two materials with densities 1 ρ and 2 ρ with 1 ρ > 2 ρ , with the area of the inner circle equal to the area of the outer shell, A c = A s , and the same forces. Also, the total mass of each disk is the same. (a) The torque about the disk center is R s F for the disks 1 and 2, and it is R c F for the disk 3. The inner circle is smaller than the outer, so . 3 , 2 , 1 , com com com τ τ τ > = (b) The rotational inertia of disks 1 and 3 are the same by inspection. The rotational inertia of disk 2 is smaller because it has more mass (the same area but denser material) closer to the center of mass than either disk 1 or 2. Therefore, I 1 = I 3 > I 2 . (c) The angular acceleration is τ α = I, so the larger the rotational inertia the smaller the angular acceleration for the same torque. So, disk 2 has larger angular acceleration than disk 1. Also, the larger the torque the larger the angular acceleration if the rotational inertia does not change, so disk 1 has larger angular acceleration than disk 3. Therefore, . 3 1 2 α α α > > 2. P.10.27. (a) Earth makes one rotation per day and 1 d is (24 h) (3600 s/h) = 8.64 × 10 4 s, so the angular speed of Earth is 5 4 2 rad 7.3 10 rad/s. 8.64 10 s ω π = = × × (b) We use v = ω r , where r is the radius of its orbit. A point on Earth at a latitude of 40° moves along a circular path of radius r = R cos 40°, where R is the radius of Earth (6.4 × 10 6 m). Therefore, its speed is 5 6 ( cos 40 ) (7.3 10 rad/s)(6.4 10 m)cos40 3.5 10 m/s. v R ω = ° = × × ° = × 2 2 (c) At the equator (and all other points on Earth) the value of ω is the same (7.3 × 10 –5 rad/s). (d) The latitude is 0° and the speed is 5 6 (7.3 10 rad/s)(6.4 10 m) 4.6 10 m/s. v R ω = = × × = ×
Image of page 1

Subscribe to view the full document.