The diagram below represents a thin rod of length L and mass m is attached to a solid disc of radius R =L3, and three times as massive as the rod (that is, its mass is 3m). The whole system is suspended from a frictionless pivot point located at L/4 from the top of the rod (as indicated by the cross on the diagram). The parameter values are also shown %3D below.
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- The uniform solid block in the figure has mass 47.6 kg and edge lengths a = 0.782 m, b = 1.61 m, and c = 0.108 m. Calculate its rotational inertia about an axis through one corner and perpendicular to the large faces. Rotation axis Number UnitsA hanging weight, with a mass of m, = 0.375 kg, is attached by a string to a block with mass m, = 0.865 kg as shown in the figure below. The string goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R, = 0.0200 m, and an outer radius of R, = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is u, = 0.250. At the instant shown, the block is moving with a velocity of v, = 0.820 m/s toward the pulley. Assume that the pulley is free spin without friction, that the string does not stretch and does not slip on the pulley, and that the mass of the string is negligible. (a) Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown. 1.517 You may have modeled the pulley as a very thin hollow cylinder with a radius of Ra, or as a…In the figure, a small 0.131 kg block slides down a frictionless surface through height h = 0.815 m and then sticks to a uniform vertical rod of mass M = 0.262 kg and length d = 2.20 m. The rod pivots about point o through angle before momentarily stopping. Find 0. A ₂ 0
- The diagram shows a thin rod of uniform mass distribution pivoted about one end by a pin passing through that point. The mass of the rod is 0.540 kg and its length is 1.20 m. When the rod is released from its horizontal position, it swings down to the vertical position as shown. Ĵ L/2 CG M (a) (a) Determine the speed of its center of gravity at its lowest position in m/s. m/s (b) When the rod reaches the vertical position, calculate the tangential speed of the free end of the rod in m/s. m/sYou are riding your bicycle down the street at a speed of 16 m/s. Your bicycle's frame has a mass of 6.0 kg, and each of its two wheels has mass 2.2 kg and radius 0.34 m. Each wheel can be thought of as a hollow hoop (assuming that the rim has much larger mass than the spokes). What is the total kinetic energy of the bicycle (in Joules), taking into account both the translational and rotational motion?A vertical rectangular object of uniform mass M = 7 kg has sides a = 0, 26 m and b = 0,58 m. It is pivoted from point O as shown in the figure below. If a constant force of F = 109 N along the diagonal is applied as shown below, determine the angular acceleration of the rectangle in SI units at the instant shown. Express your answer using one decimal place. Please use the convention: Clockwise (+), Counterclockwise (-) when expressing your answer. Hint 1: The moment of inertia of a uniform disk about an axis of rotation passing through the center of mass (CM) is ICM = 1½M(a²+b²). Hint 2: Don't forget the force of gravity!!! Take g = 9.80 m/s². a CM 0 b F
- The uniform solid block in the figure has mass 25.9 kg and edge lengths a = 0.763 m, b-1.40 m, and c=0.114 m. Calculate its rotational inertia about an axis through one corner and perpendicular to the large faces. Rotation asis Number UnitsThe outstretched hands and arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center ( Ibar=ml² where l is the length of the bar). When the skater's hands and arms are brought in and wrapped around their body to execute the spin, the hands and arms can be considered a thin-walled hollow cylinder. The hands and arms have a combined mass 10 kg. When outstretched, they span 2.1 m. When wrapped, they form a cylinder of radius 21 cm. The moment of inertia about the rotation axis of the remainder of the body is constant and equal to 0.6 kg-m2. If the original angular speed is 0.5 rev/s, what is the final angular speed? 00f= rev/s Determine how much the figure skater's rotational KE increased. [NOTE: We express energy in J. To get J, you must convert your angular velocities to the appropriate mks. units which are rad/s.] ΔΚΕ- =A hanging weight, with a mass of m, = 0.370 kg, is attached by a cord to a block with mass m, = 0.860 kg as shown in the figure below. The cord goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R, = 0.0200 m, and an outer radius of R, = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is Hy = 0.250. At the instant shown, the block is moving with a velocity of v, = 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the cord does not stretch and does not slip on the pulley, and that the mass of the cord is negligible. R2 R (a) Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown. m/s (b) What is the angular speed of the pulley (in rad/s) after the block has moved this distance?…
- The uniform solid block in the figure has mass 39.8 kg and edge lengths a = 0.902 m, b = 1.67 m, and c = 0.141 m. Calculate its rotational inertia about an axis through one corner and perpendicular to the large faces. Number: Unit:A horizontal 810-N merry-go-round of radius 1.60 m is started from rest by a constant horizontal force of 55 N applied tangentially to the merry-go-round. Find the kinetic energy of the merry-go-round after 2.0 s. (Assume it is a solid cylinder. Also assume the force is applied at the outside edge.) ____J