While the system shown is in equilibrium, a counter- clockwise torque T = To sin (wt) N-m (with To =226.6 and w =7) is applied to the disk. What is the disk angular speed %3D Wm = é in rad/s at time t = 4.2 sec? T rope viscous friction b I =0.2 kg.m?, 6 =7.8 N-m-s/r, k =1,504 N/m, r =0.52 m.

A motor (which is not shown in the figure) rotates the rod OB about the z-axis. The torque applied by the motor is given as T = 0.4 Nm. The rod OB is rotating at 3 rad/s at that instant which R = 0.4 m. And a rope attached to the slider A is let out at the constant rate of 0.25 m/s. What is the angular velocity after 10s?(Please neglect the mass of rod OB).

4а. Show that the torque t = la, where I is the rotational inertia. Consider the pulley system shown in figure 4. Suppose the pulley is made up of a disc with mass Ma and a ring (hoop) with mass M, as shown in Figure 4a. Find the moment of inertia I, of the pulley through the center of mass. 4b. Find the angular acceleration a, of the pulley as a function of Ip, 0, M1, M2, µk. You may assume that there is no slipping between the pulley and the rope and the mass of the rope is negligibly small in comparison with the mass M1, and M2. The coefficient of friction between M2 and the incline is µk with M1> M2. 4c. Mr md MK outer ving (Mr) Central dise (Ma) RI axis at RAzti on X- Sedi on a pullag

A wheel in fixed axis rotation spins at 300 rpm and decelerates at α = 3 rad/s2. How long does it take for the wheel to come to a complete stop?

Consider the disk and axle shown below. The axle has a constant angular velocity (in rad/s) in the inertial frame given by: A/N = 0.152 i. The disk has an angular velocity (in rad/s) in the axle frame given by: p/A 0.504 k . Calculate the magnitude of angular acceleration of the disk in the inertial frame (in rad/s?). N D

finished in an analytical way