Question 01 - (a) in Figure 01(A), you see a thin disk of radius, R, with constant areal mass density, o. W it were to r

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Question 01 A In Figure 01 A You See A Thin Disk Of Radius R With Constant Areal Mass Density O W It Were To R 1 (59.75 KiB) Viewed 43 times

Question 01 - (a) in Figure 01(A), you see a thin disk of radius, R, with constant areal mass density, o. W it were to rotate about the center point, use the definitional relationship that I = Srºdm to find the resulting moment of inertia in terms of o and R. (5 points) (b) What is the resulting moment of inertia in terms of the total mass of the disk, M, and the radius of the disk, R? (5 points) (c) In Figure 01(B), we now see that the same disk (of length R, mass M, and constant areal mass density o) is now pinned to the floor at a different point, 0.5OR from the center of the disk. Use the parallel axis theorem that I = Icom + MD to determine the moment of inertia about this new rotational axis. (5 points) (d) In Figure 01(C) we see that now there is also a firecracker placed at the rim of the disk such that it exerts a constant force, F, tangential to the rim of the disk. What is the resulting magnitude of the angular acceleration of the disk? Please answer in terms of R, M, and F. You may ignore any effects of friction (5 points) (e) If the disk begins its rotational acceleration from rest, after how much time, At, will the angular speed of the disk have a magnitude of ar? Please answer in terms of R, M, F, and you may still ignore any effects of friction. (5 points) (6) Plug in values R=2.0 m, M = 4,0 kg (or o = (1.0/):kg/m', if you prefer), w = 1.5 rad/s, and F-3.5-N being careful to show your work. Do the resulting units for the time required, At, make sense? Explain. (1 point of extra credit) Figure 01(A) - Disk of constant areal Figure 01(B) - Top-down view of Figure 01(C)- Top-down view of disklaying on mass density, o, shown centered on disk laying on frictionless floor and frictionless floor and pinned to the floor at 0.50R from the xy plane. The rotation axis is pinned to the floor at 0.50R from center, A firecracker is oriented such that it exerts a constant force, F, tangential to the rim of the disk as shown here parallel to the taxis at the center of the disk Y Firecracker exerting y constant force tangential у center shown below to rim of disk R 0 R X Х R Х R/2 R/2 Pin-Disk is free to rotate about this point Pin - Disk is free to rotate about this point