The structure shown in the figure is formed by a uniform ring of mass M = 1.4 kg and radius R = 20.0 cm that has particles of mass m = 90 g attached to its periphery. The hoop is welded to a uniform metal rod m of mass M and length L = 4R. The arrangement can rotate with respect to an axis perpendicular to the plane of the sheet that passes through point O located in the middle of the rod. Calculate the moment of inertia of the ring-particle-rod system. m M cm R L=4R m 0 M
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- A thin circular disc is fitted to a shaft as shown in figure. Weight of the disc is 500 N and diameter is 1.2 m. Shaft rotates at 300 r.p.m in anticlockwise direction when seen from the right side. Find the effect of the gyroscopic couple on the shaft and the bearing reactions at A and B taking the effect of the weight of the disc. 1 m. 1.5 m FigureA bar is attached to the spring at the point C. The left end of the bar is pin supported and can rotates about the pin at Point A. The mass of the bar is m=20kg. The total length of the bar is LAB=3m and LAC=2m. Point A is 0.6 m below the ceiling. A clockwise constant couple moment M= 30Nm is applied on the bar so that the bar rotates from the horizontal position with θ=0° to the vertical position with θ=90°. The spring always maintains at the vertical position. The spring’s stiffness coefficient is k=30N/m and its unstretched length is 0.5 m. The acceleration due to gravity g=9.81 m/s2. During the process that the bar rotates from the horizontal position (state 1) to the vertical position (state 2), determine the following. 5) when use T to represent kinetic energy, V potential energy, U work done and if the bar is at rest at state 1, the principle of work-energy in this case could be expressed as____________ . V1+∑U(1-2)=T2+V2 T1+V1=T2+V2…A bar is attached to the spring at the point C. The left end of the bar is pin supported and can rotates about the pin at Point A. The mass of the bar is m=20kg. The total length of the bar is LAB=3m and LAC=2m. Point A is 0.6 m below the ceiling. A clockwise constant couple moment M= 30Nm is applied on the bar so that the bar rotates from the horizontal position with θ=0° to the vertical position with θ=90°. The spring always maintains at the vertical position. The spring’s stiffness coefficient is k=30N/m and its unstretched length is 0.5 m. The acceleration due to gravity g=9.81 m/s2. During the process that the bar rotates from the horizontal position to the vertical position, determine the following. (4) the work done by the reaction force of the pin.____________ (J)
- A bar is attached to the spring at the point C. The left end of the bar is pin supported and can rotates about the pin at Point A. The mass of the bar is m=20kg. The total length of the bar is LAB=3m and LAC=2m. Point A is 0.6 m below the ceiling. A clockwise constant couple moment M= 30Nm is applied on the bar so that the bar rotates from the horizontal position with θ=0° to the vertical position with θ=90°. The spring always maintains at the vertical position. The spring’s stiffness coefficient is k=30N/m and its unstretched length is 0.5 m. The acceleration due to gravity g=9.81 m/s2. During the process that the bar rotates from the horizontal position to the vertical position, determine the following. (2) ) the work done by the couple moment. __________(J) (two decimal places)A bar is attached to the spring at the point C. The left end of the bar is pin supported and can rotates about the pin at Point A. The mass of the bar is m=20kg. The total length of the bar is LAB=3m and LAC=2m. Point A is 0.6 m below the ceiling. A clockwise constant couple moment M= 30Nm is applied on the bar so that the bar rotates from the horizontal position with θ=0° to the vertical position with θ=90°. The spring always maintains at the vertical position. The spring’s stiffness coefficient is k=30N/m and its unstretched length is 0.5 m. The acceleration due to gravity g=9.81 m/s2. During the process that the bar rotates from the horizontal position to the vertical position, determine the following. (3) the potential energy of the spring when AB is vertical__________(J)A bar is attached to the spring at the point C. The left end of the bar is pin supported and can rotates about the pin at Point A. The mass of the bar is m=20kg. The total length of the bar is LAB=3m and LAC=2m. Point A is 0.6 m below the ceiling. A clockwise constant couple moment M= 30Nm is applied on the bar so that the bar rotates from the horizontal position with θ=0° to the vertical position with θ=90°. The spring always maintains at the vertical position. The spring’s stiffness coefficient is k=30N/m and its unstretched length is 0.5 m. The acceleration due to gravity g=9.81 m/s2. During the process that the bar rotates from the horizontal position to the vertical position, determine the following. (1) if datum is set as when θ=90°, the gravational potential energy of the bar when AB is horizontal will be ____________(J) (two decimal places)
- Consider the object shown in the figure, composed of a bar (length L0=6.7 cm and mass m=84 g) connected at one of its ends to a thin plate of dimensions a=L0/2 and b=L0, and mass M =28.0 g. As illustrated in the figure, we can rotate the object around the free end; see the dashed line. In this case, what is the object's moment of inertia? Consider that both the bar and the plate have a homogeneous mass distribution, and that the axis of rotation is parallel to the plane side b of the plate. Choose one: a. None of the others alternatives. b. 2598 g.cm² c. 3896 g.cm² d. 5195 g.cm² e. 1299 g.cm² f. 1948 g.cm² g. 4546 g.cm² h. 3247 g.cm²A counterweight of mass m = 4.30 kg is attached to a light cord that is wound around a pulley as shown in the figure below. The pulley is a thin hoop of radius R = 7.00 cm and mass M = 2.80 kg. The spokes have negligible mass. m (a) What is the net torque on the system about the axle of the pulley? magnitude N. m direction Select-- (b) When the counterweight has a speed v, the pulley has an angular speed w = v/R. Determine the magnitude of the total angular momentum of the system about the axle of the pulley. kg • m)v (c) Using your result from (b) and 7 = dL/dt, calculate the acceleration of the counterweight. (Enter the magnitude of the acceleration.) m/s2A uniform rod of length L mass M which is attached at one end to a frictionless pivot and is free to rotate about the pivot in the vertical plane as shown in figure. Find the location on the rod at which you can place 1 kuruş that will stay in contact as the rod is released. -L- d=? AURE Pivot Mg
- An oversized yo-yo is made from two identical solid disks each of mass M = 1.90 kgand radius R = 10.9 cm.The two disks are joined by a solid cylinder of radius r = 4.00 cm and mass m = 1.00 kg as in the figure below. Take the center of the cylinder as the axis of the system, with positive torques directed to the left along this axis. All torques and angular variables are to be calculated around this axis. Light string is wrapped around the cylinder, and the system is then allowed to drop from rest. Answer these parts: (g) Eliminate ? from the rotational second law with the expression found in part (d) and find a symbolic expression for the acceleration a in terms of m, M, g, r and R. a = (h) What is the numeric value for the system's acceleration? m/s2(i) What is the tension in the string? N(j) How long does it take the system to drop 1.17 m from rest? sAs shown, an L-shaped bar is supported by a pin at joint A. The bar's dimensions are aaa = 620 mmmm and bbb = 400 mmmm , and the bar is subjected to a force with magnitude FFF = 5.05 kNkN at joint B. Ignoring the bar's weight, find the actual orientation of the applied force. What is the value of the angle θθtheta?0.37 kg, A machine part as shown in following figure consists of three disks linked by light weight struts. Use mA mB = 0.51 kg, mc = 0.2 kg, a = 0.59 m, b = 0.82 m and c = 1.0101980004 m. Axis through disks B and C B mB C а Axis through disk A (perpendicular to plane of figure) A mc b mA a) What is this body's moment of inertia in kg/m2 about an axis through the centre of disk A, perpendicular to the plane of the diagram? Insert your answer correct up to at least a third decimal place. b) What is the moment of inertia in kg/m2 about an axis through the centres of disk B and C? Insert your answer correct up to at least a third decimal place. c) What is the body's kinetic energy in Joule if it rotates about the axis through A with angular speed w = 72 rad/s? Insert your answer correct up to at least a third decimal place.