400 kg 6 m 8 m A 100 kg 50 kg 1a. Calculate the coordinates for the center of mass for the above object. Note that a coordinate system has been provided for you. Make an “x" at the approximate location of the center of mass in the above figure. 1b. Calculate the moment of inertia of this object about an axis that passes through the center of mass and is perpendicular to the paper.
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- Number 5 got a response saying it was incomplete but that's what I got so what?A block of mass m hangs from a string. The string is wound around a heavy wheel of mass mw and radius R. The moment of inertia of the wheel is I = mw R2 The wheel will not move horizontally or vertically, but is free to rotate without friction about its axis. The string does not slip. This question has no numbers! a) Draw free body diagrams for both the block and the wheel. Write Newton’s 2nd Law for each. b) What is the relationship between the acceleration of the block (a) and the angular acceleration of the wheel (α)? c) Use your results from part a) and b) to find the tension in the string. Please write your answers in terms of the given variables (m, mw, R, and g) only. The Earth rotates around its axis once per day. For now, the mass of the polar ice caps is located near the North and South poles. If the ice caps were to melt, this mass would move closer to the equator. EXAM d) Would melting ice caps cause the length of the day to get longer, shorter, or stay the…Consider the system shown below where four point masses are connected to each other by massless rods. Two of the masses are m = 3 kg and the other two have the masses of M = 2 kg. If a = 1.4 m, b = 1.3 m and the system rotates about x-axis, determine the moment of inertia of the system. Express your answer in units of kg. m² using one decimal place. Answer: M a m m b b a M-x
- 8. The image below depicts a street light standard that has been blown off of vertical by high winds during storm. A force of 1000N is being applied to the standard in order to "upright" the standard. Determine the magnitude and sense of the Moment about point A at the instant depicted. N-m. Be sure to include whether the Moment is Moment = Positive or Negative for this 2D problem. B 6 m 75° 3 mWhat is the magnitude of the angular momentum of the 2.40 kgkg , 4.20-cm-diameter rotating disk in the figure (Figure 1)?If an astronaut on the International Space Station accidentally left a wrench in space, the wrench would burn up as it re-entered the Earth's atmosphere, long before it hit the Earth. This question is about what would happen before that. Figure 1 Before After A wrench with a mass of 0.29 kg began at rest at a distance of d1 = 4.12 x 10° meters from the center of the Earth. The wrench then began falling toward Earth. Sometime later, the wrench was at a distance of d2 = 3.98 x 10° meters from the center of the Earth. Assume that the only significant force acting on the wrench was the gravitational force exerted by the Earth. The mass of the Earth is 5.97 x 1024 kg. Newton's gravitational constant is G = 6.67 x 1011 m³/(kg s²) (the denominator is kilograms to the first power times seconds squared) Calculate the speed of the wrench in units of meters per second when it is at a distance d2 from the center of the Earth.
- Part A What is the angular momentum of a figure skater spinning at 2.6 rev/s with arms in close to her body, assuming her to be a uniform cylinder with a height of 15 m a radius of 16 cm, and a mass of 52 kg ? Express your answer using three significant figures and include the appropriate units. L= Value Submit Request Answer Units wg ?Part A Determine the magnitude of the moment of the force F = {320i 200j + 160k}N about the x axis. (Figure 1) Express your answer to three significant figures and include the appropriate units. ? M = Value Units Figure < 1 of 1 Submit Request Answer Provide Feedback Ne: 0.3 m 0.4 m 0.2 m FSuppose we want to calculate the moment of inertia of a 65.5 kg skater, relative to a vertical axis through their center of mass. a. First calculate the moment of inertia (in kg⋅m2) when the skater has their arms pulled inward by assuming they are cylinder of radius 0.125 m. b. Now calculate the moment of inertia of the skater (in kg⋅m2) with their arms extended by assuming that each arm is 5% of the mass of their body. Assume the body is a cylinder of the same size, and the arms are 0.875 m long rods extending straight out from the center of their body being rotated at the ends.
- 17. A bullet traveling with an initial speed vo enters an door imbedding Hinge itself from the side opposite the hinges, as shown in the overhead view of the figure. Ignoring air resistance and the friction due to the hingers, which of the following statements must be true? a. The angular momentum of the system consisting of the -18.0 kg door and the bullet is conserved. b. The linear momentum of the system consisting of the door and the bullet is conserved. 0.005 kg c. The total mechanical energy of the system consisting of the door and the bullet is conserved. d. The total kinetic energy of the system consisting of the door and the bullet is conserved.9. Figure 4.24 shows a beam with four forces acting on it. For each force, calculate the moment of the force about point P. a State whether each moment is clockwise or anticlockwise. C State whether or not the moments of the force are balanced. F, = 10 N F4 = 5N -25 cm- -25 cm- -50 cm 30° F2 = 10 N F3 = 10 N Figure 4.24: For Question 9.