Rolling Motion (Free Wheels) Practice Problems

A sphere initially at rest is spun in a circle at an angular acceleration α. The sphere's acceleration vector changes as a function of time. Determine the time when the angle between the radius and acceleration vector is θ degrees. Express t in terms of α and θ.

Calculate the moment of inertia for three wind turbine blades considered as thin rods, each 3.76 m long and with a mass of 133 kg, about the rotation axis.

Calculate the total kinetic energy of a 7.5 kg soccer ball with a 9.1 cm radius that rolls without slipping down along a track at 3.9 m/s.

A 450-kg wheel with a diameter of 2.5 m got detached from a vehicle and started rolling without slipping on a flat surface to the left at a constant angular speed of 1.5 rad/s. Determine the velocity vector for each point on the wheel as observed by someone moving along with the same velocity as the center of the wheel: i) the topmost point of the wheel ii) the point in contact with the ground iii) the leftmost point on the wheel.

Initially resting on a frictionless ice rink, a solid uniform steel disk with a mass of 25.0 kg and a radius of 60.0 cm is pulled by a rope wound around its circumference. A constant horizontal force of 30.0 N is applied to the rope, pulling it to the right. In which direction does the center of mass (CM) of the disk move?