A 2-mm-thick piece of sheet steel is cut and bent into the machine component shown. Knowing that the density of steel is 7850 kg/m³, determine the mass moment of inertia of the component with respect to each of the coordinate axes. 195 mm 350 mm 150 mm
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- A thin, hollow sphere of radius r = 0.480 m and mass m = 16.0 kg turns counterclockwise about a vertical axis through its center (when viewed from above), at an angular speed of 2.90 rad/s. What is its vector angular momentum about this axis? (Enter the magnitude in kg. m²/s.) kg-m²/s magnitude direction ---Select--- vA thin rod of length L = 5 m and mass m has a linear density A(x) = Ax³ where x is the distance from the rod's left end. X(x) has units of kg/m and A = 6.38 with appropriate units that can't be displayed nicely due to Canvas limitations. Calculate the rod's moment of inertia I about an axis through x = 0 and perpendicular to the rod's length. (Hint: Evaluate the integral I = fr² dm where r = x is the distance from the axis to each element of mass dm = X(x) dx . Note: The rod's total mass mass m isn't needed but, if you would like to know it, you can find it by evaluating the integral m = f dm = f(x) dx.) I= kg m²4 spheres, each of diameter D= 0.05 m (spheres are identified as 1, 2, 3, 4), are placed on the end of 4 rods of length L = 0.15 m, arranged in a cross pattern as shown in the figure. L The rigid assembly is free to pivot without friction about the axis, o, normal to the page. Sphere 1 is covered with roughness of height ɛ = 0.25 mm while all other spheres are smooth. 1 With an oncoming velocity of U= 60 m/s, which direction will the assembly rotate? (Clockwise or counterclockwise). Use appropriate calculations to explain and justify your answer. Density of air is 1.2 kg/m³ and viscosity is 1.5 x 10-5 m²/s. 3.
- A solid uniform 45-kg ball of diameter 32.0 cm is supported against a vertical, frictionless wall with a string of length 30.0 cm as shown below. Find the tension in the string.Vlad needs to draw water from a deep well. He is using a bucket that is connected by rope (negligible mass) to a wooden axle at the top of the well. By cranking a handle at the end of the axle, Vlad is able to unwind the rope around the axle and move the bucket downward. The radius of the axle is R = 30 cm. The bucket is traveling downward at speed vi = 25 cm/s when the handle slips out of Vlad’s hand. As the rope unwinds and the bucket falls downward, the axle spins freely with an angular acceleration whose magnitude is α = 4.5 rad/s^2. The bucket falls through a distance of d = 7.0 m before crashing into the water. 1. What is the angular speed ωf of the axle when the bucket first hits the water? 2. As d → 0, what limit does ωf approach and why?Problem 7: Consider the 10.5 kg motorcycle wheel shown in the figure. Assume it to be approximately a ring with an inner radius of 0.28 m and an outer radius of 0.33 m. The motorcycle is on its center stand, so that the wheel can spin freely.
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