If a body is rolling on another body, the linear and angular motions of the body are constrained by one another the relative velocity of the points in contact is zero the magnitude of friction force is less than or equal to u*N the friction force leads to loss of energy

Please show all work and diagrams! Anything is helpful.

A cylinder of radius r = 0.15m and massm-8kg with an initial counterclockwise angular velocity w 5rad/s is placed in the corner formed by the floor and a vertical wall. The coefficient of kinetic friction between the cylinder and the wall and the floor is HK-0.12. W1 G m 1) Draw the Momentum and impulse diagrams. 2) Find the normals forces and the friction forces. 3) Determine the time required for the cylinder to come to rest. In the box below enter the time t in seconds with 1 decimal required to come to rest.

A solid sphere of mass M and radius R rolls without slipping along a table at speed v. What is its kinetic energy? Mv2/5 Mv2/2 Mv2 3Mv2/2 7Mv2/10

Determine the number of degrees of freedom in the following mechanical systems: (a) a compact disc in use (i.e., a rigid body revolving about a fixed axis—all points along the axis remain stationary), (b) a spinning top (i.e., a rigid body rotating about a fixed point—all points on the body may rotate except for the fixed point), (c) a crawling insect on the ground (i.e., a particle moving on a given surface)

A box of mass m = 0.7 kg is attached to a rope which is wrapped around a physical pulley with a radius of R = 10.2 cm and a rotational inertia of I = 0.075 kg·m2. When the box is released it starts to fall down with a constant acceleration and, at the same time, the pulley starts to spin up, see the picture below. Assuming that the pulley is frictionless, what is the magnitude of the box's acceleration and what is the tension in the rope?   The acceleration of the box, a ? The tension in the rope, T? If the box starts from rest and traveled downwards a distance of h = 28 cm, what is the speed of the box and what is the angular velocity of the pulley? The speed of the box, v =? The angular velocity of the pulley, ω? -------------------------------------------------------------- A Merry Go Round carousel has a radius of R = 2.4 m and a rotational inertia of I = 695 kg·m2. A 75‑kg student is on the carousel at the midpoint between the carousel's center and the rim (at R/2 distance from…