Problems 3.64 and 3.65 The system shown is initially at rest when the bent bar starts to rotate about the vertical AB with constant angular acceleration a, = ombetween the collar of mass m = 3 rad/s. The coefficient of static fric- 2 kg and the bent bar is u, 0.35, and the collar is %3D tally d = 70 cm from the spin axis AB. Problem 3.64 Assuming the motion starts at t = 0, determine the time at which the allar starts to slip relative to the bent bar. Figure P3.64 and P3.65

Question 2: A point-mass M of mass m is tied to a string which winds around a cylinder like a bobbin. The string is pinned on the cylinder at some point, and P denotes the point at which the string leaves the bobbin and starting from which it is taut. The cylinder has radius a and rotates at a constant rate around the vertical axis of the fixed frame F (which is also the axis of symmetry of the bobbin). The motion takes place in the hori- zontal plane, which is assumed frictionless. See figure. (a) Find a relationship between l, a and expressing that the length of the string is constant (b) Compute the velocity and acceleration of point M with respect to F. (c) Apply LMB in F to the system consisting of the point mass M alone (don't forget to start with a free body diagram!). Deduce a differential equation for l as well as the value of the string's tension in terms of the other parameters. (d) (bonus) Solve the differential equation for l. eo Ω Mas P M FIGURE 1 - The spinning bobbin.…

(97) Derive the equations of motion of the system shown in the figure below using Lagrange's equation. The circular cylinder has a mass m and radius r rolls without slipping inside the circular groove of radius R. m, M

QUESTION 14 The collar of mass m = 77 kg in Figure Q14 slides outwards with an initial radial velocity vo = 0.58 m-s-1 from zero initial radial position (see dashed box) along a smooth rotating shaft (see unit vector ur). The shaft rotates with constant angular speed of w = 2 rad-s-1. Determine the magnitude of the constant force F (N) that needs to be applied in the radial direction (pointing towards the centre of the shaft) in order to decelerate the collar to zero radial velocity the moment when the collar reaches a radial position r = 0.19 m. Consider motion in a horizontal plane, such that gravity can be ignored. Provide only the numerical value (in Newtons) to zero decimal places and do not include the units in the answer box. Ur F m Vo Figure Q14: Rotating collar-shaft system