The uniform thin rod of mass 1.8 kg per meter of length is bent into the shape shown. If a =0.4 m and b =1.7 m, determine the moment of inertia of the rod about the x-axis shown. Give your answer in kg.m?.
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- A rope with a negligible mass has two blocks that are suspended over a pulley, m, and M, as shown in the image. The pulley can be considered as a uniform solid cylindrical disk. What is the equation for the net torque on the disc? Assume acceleration of blocks are a=(1/2)(9.8m/s2). What is the moment of inertia for this shape? (using the net torque equation from the above question, substitute the moment of inertia) The angular acceleration is correlated to the linear acceleration as α=r. Make the substitution into the torque equation in order to get the equation in terms of acceleration, α only.A ballerina spins initially at 1.56 rev/s when her arms are extended. She then draws in her arms to her body and her moment of inertia becomes 0.82 kg-m², and her angular speed increases to 4.43 rev/s. What was her initial moment of inertia? Give your answer in kg-m².A thing solid cylinder has a mass 6.98kg and a length 1.66 m. What is its moment of inertia (in unit of kg.m2) when it is rotating as shown above? (please search your physics text book or other sources for the correct formula for this situation, you lab manual does not necessarily have the formula.)
- PLEASE DRAW AN FBD AND ANSWER IT ON A PAPER The figure shown is on a fixed frictionless axle. It has a moment of inertia of I = 50 kg-m2 . The forces acting on the object are F1 = 100 N, F2 = 200 N, and F3 = 250 N acting at different radii R1 =60 cm, R2 = 42 cm, and R3 = 28 cm. Determine the angular acceleration of the object.An approximate model for a ceiling fan consists of a cylindrical disk with four thin rods extending from the disk's center, as in the figure below. The disk has mass 2.30 kg and radius 0.200 m. Each rod has mass 0.850 kg and is 0.840 m long. HINT (a) Find the ceiling fan's moment of inertia about a vertical axis through the disk's center. (Enter your answer in kg. m².) kg - m² (b) Friction exerts a constant torque of magnitude 0.113 Nm on the fan as it rotates. Find the magnitude of the constant torque provided by the fan's motor if the fan starts from rest and takes 15.0 s and 16.5 full revolutions to reach its maximum speed. (Enter your answer in N. m.) N.mA circular disk with a radius of 0.45 m is subject to 2 tangentially applied forces. The disc is fixed such that it will rotate about its center. Both forces produce a torque in the same direction. The mass of the disc is 0.59 kg. The moment of inertia of a disc is I MR? F1 = 2.3 N applied at the outer edge of the disc. %D F2 = 4.3 N applied at a distance of 0.21 from the center of the disc. What is the angular acceleration of the disc?
- A typical helicopter with four blades rotates at 370 rpm and has a kinetic energy of 7.05 x 105 J. What is the total moment of inertia, in kg. m² of the blades?Consider the setup shown below. The blocks have masses 3.6 kg and 24 kg. The pulley has mass 7.4 kg, and is a uniform disc with radius 0.23 m. Assume the pulley to be frictionless, but the coefficient of friction between the block and the surface is 0.36. What is the acceleration of the blocks? Assume the 24 kg mass is descending with acceleration a. The moment of inertia of the disk is 1/2MR2 and the acceleration of gravity is 9.8 m/s2.A soccer player extends her lower leg in a kicking motion by exerting a force with the muscle above the knee in the front of her leg. Suppose she produces an angular acceleration of 32.5 rad/s2 and her lower leg has a moment of inertia of 0.75 kg⋅m2 . What is the force, in newtons, exerted by the muscle if its effective perpendicular lever arm is 2.1 cm? F =
- A top has a moment of inertia of 10.7 kg-m2. The top is spinning at 41 rpm. How much rotational kinetic energy (in joules) does the top have?A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 280 N applied to its edge causes the wheel to have an angular acceleration of 0.946 rad/s2. What is the moment of inertia of the wheel? What is the mass of the wheel? If the wheel starts from rest, what is its angular velocity after 5.40 s have elapsed, assuming the force is acting during that time?