A body has mass 450 g .when it revolves in a circle of radius 2m.The body makes 2 revolution per second . the centripetal force is : *
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- The chain OA is 25 ft long and weighs 5 lb/ft. Find the maximum force in the chain and the distance H.A uniform solid disk of mass 2.0 kg and radius 0.30 m is initially at rest. It is then rotated by a constant torque about an axis through its center of mass until it reached an angular speed of 3.0 rad/s. What is the work done by the constant torque? The moment of inertia through the center of mass is (2/5)MR^2.The disk with a diameter of 20cm and a mass of 300g and the border of a disk-shaped object with a diameter of 30cm and a mass of 600g are interlocked. Apply a force of 9 N to the outer circumference of the small disk and rotate the two plates together. Find each torque applied to the small disk and the torque applied to the large disk.
- The figure below is a system consisting of two masses MA = 1.82 kg and MB = 3.6 kg, whose distance from the pore axis is R₁ = R₂ = 15 cm, while the angular positions are 0₁ = 30° and 0 = 150° . Determine the weight and position of the balancing mass placed on planes C and D if the distance from the axis RC = RD = 15 cm.The frame of a gyroscope in fig. is supported at O so that it can turn freely in alldirections. The wheel is a uniform disc of 10 cm diameter weighing 2 kg with its centre20 cm from O. The frame alone weighs 1 kg with centre of gravity G1, 12 cm from O.If the wheel spins as shown at 10,000 r.p.m. with its axle in the horizontal plane, findthe time required for the axle to make one revolution about O. Mention the direction ofthis rotation. Find also the vertical and horizontal forces by the support on the frame.A uniform rod of mass M = 2.3 kg and length L = 0.2 m, lying on a frictionless horizontal plane, is free to pivot about a vertical axis through one end, as shown. The moment of inertia of the rod about this axis is given by 1/3 ML2. If a force F = 7 N, q = 47° acts as shown, what is the resulting angular acceleration (in rad/s2) about the pivot point?
- Blocks A and B shown in the figure have masses of 5 kg and 10 kg respectively.If the pulley is treated as a 3 kg solid disk with a 15 cm radius, determine the acceleration of the block A. Disregard the rope mass and any slip on the pulley.Consider that the moment of inertia of the pulley is given by Ip = (1/2)mr² in which m is the mass of the pulley and r is of radius the pulley.A forklift and its driver have a total weight of 50000 and the center of mass in at G. What is the reaction force on each of the wheels when the 8000 weight load is pulled up with an acceleration of 1.5 m/s^2? (a= 1.2 meter, b= 0.9 meter, c= 1.7 meter, h= 3.5 meter)A shaft with 3 meters span between two bearings carries two masses of 10 kg and 20 kg acting at the extremities of the arms 0.45 m and 0.6 m long respectively. The planes in which these masses rotate are 1.2 m and 2.4 m respectively from the left end bearing supporting the shaft. The angle between the arms is 60°. The speed of rotation of the shaft is 200 r.p.m. If the masses are balanced by two counter-masses rotating with the shaft acting at radii of 0.3 m and placed at 0.3 m from each bearing centers, estimate the magnitude of the two balance masses and their orientation with respect to the X-axis, i.e. mass of 10 kg Note: It must be solved using the graphic method, not the equations method.
- A shaft with 3 meters span between two bearings carries two masses of 10 kg and 20 kg acting at the extremities of the arms 0.45 m and 0.6 m long respectively. The planes in which these masses rotate are 1.2 m and 2.4 m respectively from the left end bearing supporting the shaft. The angle between the arms is 60°. The speed of rotation of the shaft is 200 r.p.m. If the masses are balanced by two counter-masses rotating with the shaft acting at radii of 0.3 m and placed at 0.3 m from each bearing centers, estimate the magnitude of the two balance masses and their orientation with respect to the X-axis, i.e. mass of 10 kg.A 10 kg , 0.5 m radius wheel is to rotate from rest to a speed of 100 rad/s in 5 s. Determine the tangential force ( N ) created at the rim of the wheel.5) In ice figure skating, a couple execute a “top” (see picture). The centre of mass of the woman (58 kg) is situated 1.3 m from the axis of rotation which is vertical and passes through the centre of mass of the man (85 kg). They are spinning at a constant angular velocity equal to 3.1415 rad/s and the man and woman have moments of inertia, about their own centres of mass, equal to 1.6 and 2.5 kg.m2 respectively. Then the woman grabs the neck of the man. At this point, her moment of inertia decreases to 1.4 kg.m2 and her body centre of gravity is 0.9 m from the axis of rotation. Determine the new angular velocity. Hints: This is a conservation of angular momentum problem, and needs the parallel axis theorem to determine moments of inertia about the axis of rotation. The skaters are moving as one body with one angular velocity, but they each have their own moments of inertia given relative to their own CoMs. For the man, that’s fine…the axis they’re rotating about passes through his…