A string is wound around a uniform disk of radius R and mass M. The disk is released from rest with the string vertical and its top end tied to a fixed bar. Using kinematics, calculate: A) the tension in the string as the disk unwinds and falls, B) the acceleration of the center of mass of the disk, C) the speed of the disk after falling a distance H. D) Verify your answer to C) by using the energy method.
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A string is wound around a uniform disk of radius R and mass M. The disk is released from rest with the string vertical and its top end tied to a fixed bar. Using
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- A cylinder of mass M=8 kg and radius R=20 cm slides down a frictionless hill from height H=10 m. At the bottom of the hill there is a plane with friction coefficient u=0.25. a) How far will the cylinder slide along the plane before it begins to roll smoothly? b) What will be the final speed of the center of mass of the cylinder? No friction 10 m FrictionA large plate is initially rotating about an axis through its center with angular velocity of 3w, as shown in the figure. The upper plate is initially not rotating and has the same mass but half the radius as the large plate. The small plate is lowered onto the large plate, and after a short time they will rotate together and willI have the same final angular velocity. Which of the following best describes the ratio of the kinetic energy of the system before the collision to after the collision (Ratio KEbefore KEafter %D 3w. 1.50 1.25 1.00 0.80 0.67The paths of two small satellites, X and Y, of equal mass of 4.00 kg each, are shown below. They orbit around a massive star, as illustrated, with M = 6.20x1029 kg The orbits are in the plane of the paper and are drawn to scale. %3D a C In the statements below KE is kinetic energy, PE is potential energy, and L is magnitude of the angular momentum. At a, the PE of X is .... that of Y. v The speed of Y at c is .... that at a The L of X at p is .... that at u. At a, the KE of X is .... that of Y. The PE of Y at c is .... the PE of X at w Submit Answer Tries 0/12 Send Feedb
- Item 11 The pulley in (Figure 1) has radius 0.160 m and moment of inertia 0.380 kg - m². The rope does not slip on the pulley rim. Figure 4.00 kg 5.00 m 2.00 kg 1 of 1 Part A V = Use energy methods to calculate the speed of the 4.00 kg block just before it strikes the floor. Express your answer with the appropriate units. μÀ Value Submit Request AnswerA)Determine the angular momentum of a 73-g particle about the origin of coordinates when the particle is at x = 4.8 m , y = -5.7 m , and it has velocity υ=(3.2i^−8.1k^)m/sFind the x-component. Express your answer using two significant figures. B) Find the y-component. Express your answer using two significant figures. C)Find the zz-component.If the earth warms significantly, the polar ice caps will melt. Water will move from the poles, near the earth’s rotation axis, and will spread out around the globe. In principle, this will change the length of the day. Why? Will the length of the day increase or decrease?
- A'solid sphere of radius 9 cm is allowed to rotate freely about an axis. The sphere is given a sharp blow so that its center of mass starts from the position shown in the following figure with speed 15 cm/s. What is the maximum angle that the diameter makes with the vertical? Round your answer one decimal place. Axis Force V = 15 cm/s Hint 0= ? 0 = degrees Question Help: Message instructor Submit QuestionA 3.0-kg mass slides on a frictionless horizontal surface with a speed of 3.0 m / s when it collides with a 1.0-kg mass initially at rest as shown in the figure. The two masses stick to each other and slide on a frictionless circular wheel portion of radius 0.40 m. At what maximum height h, above the horizontal, do the masses reach? Answers: a) 0.18 m b) 0.15 m c) 0.21 m d) 0.26 m e) 0.40 mpulley m Figure 8-78 Problem 97. Type your answers in all of the blanks and submit X, ** In Figure 8-78, a rope is wound around a horizontal disk (Md = 2.90 kg and Rd = 20.0 cm), passed across a pulley (with negligible mass), and connected to a hanging 4.00 kg mass. Initially, the mass is held in place, and the system is at rest. The mass is then released and descends in response to the force of gravity. The rope does not slip on the pulley or the horizontal disk. Both the pulley and the disk rotate on bearings that are effectively frictionless. Using energy considerations, (a) find the angular speed of the disk after the mass has descended 1.20 m. Type your answer here rad/s. Please type your answer to submit (b) calculate the acceleration of the mass. Type your answer here m/s2
- 72. A body of mass m and negligible size starts from rest and slides down the surface of a frictionless solid sphere of radius R. (See below.) Prove that the body leaves the sphere when 0 = cos¹ (2/3). RA solid metal disk with moment of inertia I, radius R, and mass m1 can rotate freely about a frictionless axis passing through its center. A light string is wrapped around the disk and connects to a hanging mass m2. The hanging mass is released from rest at a distance d above the ground and accelerates downward with acceleration awhile the disk rotates through an angle q. a) Draw free body diagrams for the disk and the hanging mass. b) Find an expression for the angular accelerationaof the diskin terms of m2, I, R, and any necessary constants. c) Find an expression for the time it takes for the hanging mass to reach the ground. Write your answer in terms of q, a, and any necessary constants.A hollow cylinder (hoop), a solid cylinder (disk), and a solid sphere, each of mass M and radius R, roll down a hill of height h. Rank the objects based on their total kinetic energy at the bottom of the hill. Rank the one with the most energy 1, etc. If two are equal, give them the same ranking. hoop___________ disk_______________sphere_______________Justify your ranking