Rotational Dynamics of Rolling Motion Practice Problems

A car tire of mass 9.80 kg and radius 289 mm rolls to the right without slipping on a horizontal section of the road with a constant angular velocity of 15.3 rad/s. Determine the resultant velocity vector of the following points located on the circumference of the tire: i) the point in contact with the road; ii) the point on the left side of the tire and exactly halfway between the top of the tire and the road; iii) The topmost point on the tire.

A soccer ball is kicked along a 23° inclined plane with a speed of v = 5.0 m/s at the foot of the incline. Determine the time it takes for the soccer ball (a hollow sphere) to climb the incline and return to its original position.

A child's wooden toy has the form of a sphere. The child throws the ball so that it rolls down a surface that is inclined at an angle θ above the horizontal without slipping. If the ball behaves like a uniform solid sphere, determine the acceleration of the ball's center of mass.