The end of a string wrapped around a disk of mass M and radius R is held stationary while the disk falls and unwinds the string. The disk has a center-of-mass moment of inertia I= ½MR2. Using the sketch for reference, what direction is the angular acceleration a of the disk while it is falling? end held B) fixed gravity disk E) a|=0, so the direction is ambiguous M, R string
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- a) a b) b c) c 2. Two different disks (one is larger than the other but the same mass) are placed flat on ice. If the same force F is applied to each disk as shown. Mark the statement(s) that are correct. (a) (b) (c) (d) (e) (f) disk 1 Ⓒ disk 2 disk 1 will have more linear acceleration disk 2 will have more linear acceleration disk 1 will have more angular acceleration disk 2 will have more angular acceleration they both have the same linear acceleration they both have the same angular acceleration 1Macmillan Learning Your computer has an optical disk drive that can spin up to 10,000 rpm (which is about 1045 rad/s). If a certain disk is spun at 352.9 rad/s during the time it is being read, and then comes to rest over 0.569 seconds, what is the magnitude of the average angular acceleration of the disk? average angular acceleration: If the disk is 0.12 m in diameter, what is the magnitude of the linear acceleration of a point 1/3 of the way out from the center of the disk? linear acceleration: x10 rad/s² TOOLS m/s²Flying Circus of Physics A yo-yo has a rotational inertia of 1110 g.cm² and a mass of 94.4 g. Its axle radius is 2.47 mm, and its string is 133 cm long. The yo-yo rolls from rest down to the end of the string. (a) What is the magnitude of its linear acceleration? (b) How long does it take to reach the end of the string? As it reaches the end of the string, what are its (c) linear speed, (d) translational kinetic energy, (e) rotational kinetic energy, and (f) angular speed? (a) Number i 5.1 (b) Number i 7.2 (c) Number i (d) Number i (e) Number i (f) Number i 000 Units Units Units Units Units Units m/s^2 PHON
- can you do (c) and (d)?Diving from a high cliff, Cliff begins with a moderate rotational speed of a half rotation per second. Rank the following positions (and their moments of inertia) that cliff can assume during his dive, from the lowest rotational speed he will experience to the highest. + 1. Standing straight up, spinning about a head-to-toe axis: I = 0.3 kg m2 + 2. Bent in half, about an axis through his waist: I = 4 kg m- %3D + 3. Standing straight upwards, about an axis through his waist: I = 16 kg m2 + 4. Mass tucked inwards into a ball: I = 0.8 kg m- + 3. Arms out, spinning about a head-to-toe axis: I = 1.2 kg m21) Blocks of mass m1 and m2 are connected by a massless string that pulls over the pulley in the figure. Initially, the system is at rest. The table is frictionless. The pulley is frictionless, but it does have mass Mp and radius R. The moment of inertia of the pulley is Ipulley=2/3MR2 (note that this is DIFFERENT than what we have used in the practice test examples). Consider that at t=0 (initially) m2 is H meters above the ground. In this problem, H=60 cm., R=7 cm., Mpulley=1.8 kg, m1=6 kg, and m2=15 kg. (a)Using those energies from the above table that apply to this question and identifying the ground as the point of "zero height", use "conservation of energy" to find the speed of m2 just as it hits the ground. There are no non-conservative forces outside of the system to consider, so Ef=Ei (the initial state is when the system is at rest and m2 is hanging H meters above the ground, and the final state is when the system is moving (both blocks are moving and the pulley is spinning)…
- A mass hangs by a massless string that is wound around a solid circular pulley of radius 20 cm. There is no friction in the pulley. The block is released from rest, and the pulley goes through three complete rotations (6 t radians) in 4 seconds. 0.2 m What is the direction of the angular acceleration? A) Up B) Down C) Into the page D) Out of the page E) Unknown O A O B E.During a steady right turn, a person exerts the forces shown on the steering wheel. Note that each force consists of a tangential component and a radially-inward component. Determine the moment exerted about the steering column at O. The moment will be positive if counterclockwise, negative if clockwise. 14 31 435 mm 8.6 N 31/ 8.6 N