1. A uniform solid cylinder of mass M and radius R rolls up an inclined ramp without slipping. The initial speed of its center of mass is vi. The angle of inclination of the ramp is 0. (Icm = (1/2) MR²) (a) Draw forces acting on the cylinder and write the translational and rotational equations. Now, Take M = 0.8 kg, R = 6.0 cm, 0 = 15°, vị = 0.85 m/s, and (b) Find the angular acceleration and the linear acceleration of the center of mass of the cylinder. (c) What is the magnitude of the friction force on the cylinder? (d) How far up the ramp can the cylinder reach? (Use energy method)

1. A uniform solid cylinder of mass M and radius R rolls up an inclined ramp without slipping. The initial speed of its center of mass is vi. The angle of inclination of the ramp is 0. (Icm = (1/2) MR²) (a) Draw forces acting on the cylinder and write the translational and rotational equations. Now, Take M = 0.8 kg, R = 6.0 cm, 0 = 15°, vị = 0.85 m/s, and (b) Find the angular acceleration and the linear acceleration of the center of mass of the cylinder. (c) What is the magnitude of the friction force on the cylinder? (d) How far up the ramp can the cylinder reach? (Use energy method)