x(1) Figure 1: A uniform wheel of mass m and radius r rolling on a horizontal surface. 1. Assume that the wheel as a rigid body lives in the 3D space and that the wheel rolls without slipping, write down and classify all the constraints. 2. When the wheel rolls without slipping, how many degrees of freedom does the wheel have? Write down the kinetic energy of the wheel and find the equivalent mass of the wheel. 3. If the wheel slips, write down all the constraints and find degrees of freedom of the wheel have. Write down the kinetic energy of the wheel for this case.

x(1) Figure 1: A uniform wheel of mass m and radius r rolling on a horizontal surface. 1. Assume that the wheel as a rigid body lives in the 3D space and that the wheel rolls without slipping, write down and classify all the constraints. 2. When the wheel rolls without slipping, how many degrees of freedom does the wheel have? Write down the kinetic energy of the wheel and find the equivalent mass of the wheel. 3. If the wheel slips, write down all the constraints and find degrees of freedom of the wheel have. Write down the kinetic energy of the wheel for this case.