A wheel is fixed at its center position and allowed to rotate. The moment of inertia of the wheel is J, and the wheel is connected to the fixed center point through a torsional spring with spring constant k(subscript 1) (not shown in the above figure). This wheel is in contact with mass M. The wheel and the mass maintain rolling without sliding condition at the contacting surface. We apply a torque T at the wheel. Derive the Equation of Motion for the system. You should have only one unknown response in your equation. Use x(t) . I am having a lot of trouble with this problem - please be very detailed and explain fully!

Please solve only 4,5

A conveyor is used to drive the inertial load of 0.02 kg m² in the required speed range with a brushless DC motor and a gearhead having reduction ratio of 15:1 as shown in the figure below. The belt speed is V=1 m/s and the roller diameter is D=0.1 m. Choose the correct statement. Load Motor Right Angle Gearhead O The moment of inertia of the load referred to the motor shaft is 0.00133 kg m² O The moment of inertia of the load referred to the motor shaft is 0.0133 kg m² O The rotation speed of the motor shaft is 1665 RPM O The rotation speed of the gear shaft is 100 RPM O The rotation speed of the motor shaft is 2865 RPM.

Problem 2: A car is pushing a barrel to the right. The pushing force P is applied by the front bumper which is level with the center G of the barrel (see figure). The barrel has mass m, radius R, and radius of gyration kG. The coefficients of static and kinetic friction between the bumper and the barrel are µs and µk. The coefficients of static and kinetic friction between the barrel and the road are also µs and µk. 1) If the barrel doesn't slip on the road, find the acceleration of the barrel and the minimum value of us required to ensure no slipping. 2) If the barrel slips on the road, find the acceleration of G and the angular acceleration of the barrel. Hs. Hk. m

12 For the mechanism shown in figure, degree of I GV (b) 1 (c) 2 G

The figure illustrates a torsion-bar spring OA having a diameter d = 12 mm. The actuating cantilever AB also has d = 12 mm. Both parts are of carbon steel. Use superposition and find the spring rate & corresponding to a force F acting at B. 0.1 m 15m

The structure of a football goal is shown in the figure below. The bending motion of the structure can be represented by a flexible cantilever beam with tip mass M¡ as shown in the figure. The tip mass M, represents the mass of the horizontal crossbar which is assumed to be rigid in this motion. A single vertical straight beam having mass of MH, shown in the figure below, is the equivalent model for the two symmetrical vertical posts. A soccer ball of mass M, hits the horizontal crossbar with the velocity of Vp. x(t) м, VINGLI SOLAR The response of the horizontal crossbar, mass M, is shown by x(t) in the figure. The vertical beam has a circular cross section of radius r, Young's modulus E and length L. For numerical calculations, use M, = 23.2130 kg, MH = 28.6617 kg. M, = 0.5497 kg, Vý = 8.8974 m/s, L= 2.7757 m, E = 133.5685 GPa andr= 0.0437 m. For circular cross- section I = Tr/4.Considering zero damping and the numerical data given above, obtain the maximum amplitude of response x(t)…

Correct solution will be liked..

Consider the system shown in the figure. Disk m, rolls without slip. a is defined as the displacement of mass mo and is positive to the left. When x displaces in a positive direction, it rotates the disk (with moment of inertia J1 and radius R) by an angle 01. Use 0, to denote the rotation of the mass m, (a disk with moment of inertia J, and radius r2). Assume small displacements (and hence small rotations). Use x as the coordinate to describe this system. mo m2 ww k Syntax Use J[1],J[2], k[1].r[1].r[2],m[2] for J1 ,J9,k1.r1.r2 and m2. Use m[0] (m with subscript as the number zero) for mo- How many degrees of freedom does this system have? The system has 2 degrees of freedom - from the disk and cart that are on the horizontal surface plus the rotating disk on the left. The system has 4 degrees of freedom: translation and roation of the first disk, rotation of the other disk and translation of mass mo- O None of the other responses are correct. O The system has 3 degrees of freedom…

(3) A circular cam 8-in in diameter rotates off-center with an eccentrity e = 1" & operates the roller follower that is carried by the arm. The roller follower is held against the cam by means of a tension spring attached a third from a fixed pivot point. The force against the cam & roller follower is approximately 50lb @ the low position & 80lb @ high position. The ratio of the coil diameter to that of wire diameter is 7.0. The allowable stress on the spring is S,= 60,000psi. Calculate : P (a) the wire diameter; (b) the outside diameter of spring; (c) the number of active coils recommended.