Problem 6 - Rolling without slipping A solid ball of uniform density with mass M and radius R rolls without slipping on an incline that makes an angle of 0 with the horizontal, as shown in Fig.6. Recall that the 2MR2 moment of inertia of a solid ball about an axis passing through its center is Icm = 5 ст a) Draw an "extended" free body diagram of the ball indicating where every force acts on the ball. b) What is the angular acceleration of the ball? K-D- c) How fast is the ball's center of mass moving after it has rolled a distance D along the ramp, starting from rest? d) What is the minimum value of the coefficient of static friction u, between the ball and the ramp? e) At any moment in time, what fraction of the ball's total kinetic energy is the rotational about the ball's center of mass? kinetic Figure 6 energy

Problem 6 - Rolling without slipping A solid ball of uniform density with mass M and radius R rolls without slipping on an incline that makes an angle of 0 with the horizontal, as shown in Fig.6. Recall that the 2MR2 moment of inertia of a solid ball about an axis passing through its center is Icm = 5 ст a) Draw an "extended" free body diagram of the ball indicating where every force acts on the ball. b) What is the angular acceleration of the ball? K-D- c) How fast is the ball's center of mass moving after it has rolled a distance D along the ramp, starting from rest? d) What is the minimum value of the coefficient of static friction u, between the ball and the ramp? e) At any moment in time, what fraction of the ball's total kinetic energy is the rotational about the ball's center of mass? kinetic Figure 6 energy