PHYSICS 7C Study Guide - Final Guide: Rigid Body

the string in a yo-yo is wound around an axle of radius 0.470 cm.The yo-yo has both rotational and translational motion, like arolling object, and has mass 0.185 kg and outer radius 1.90 cm.starting from rest, it rotates and falls a distance of 1.18 m (thelength of the string). assume for simplicity that the yo-yo is auniform circular disk and that the string is thin compared to theradius of the axle.

a.) What is the speed of the yo-yo when it reaches the distance of1.18 m?

answer is in m/s.

i'm lost on how the translational and rotational energies arerelated, but the yo-yo is not rolling on its outer radius.

Three particles A, B, and C each of mass m are connected to each other by three massless rigid rods to form a rigid, equilateral triangular body of side l. This body is placed on a horizontal frictionless table (x-y plane) and is hinged at point A so that it can move without friction about the vertical axis through A (see figure). The body is set into rotational motion on the table about this axis with a constant angular velocity . (a) Find the magnitude of the horizontal force exerted by the hinge on the body. (b) At time T, when side BC is parallel to the x-axis, force F is applied on B along with BC (as in the figure). Obtain the x-component and the y-component of the force exerted by the hinge on the body, immediately after time T.

9.81 - BIO The Kinetic Energy of Walking. If a person of mass M simply moved forward with speed V, his kinetic energy would be MV. However, in addition to possessing a forward motion, various parts of his body (such as the arms and legs) undergo rotation. Therefore, his total kinetic energy is the sum of the energy from his forward motion plus the rotational kinetic energy of his arms and legs. The purpose of this problem is to see how much this rotational motion contributes to the person's kinetic energy. Biomedical measurements show that the arms and hands together typically make up 13% of a person's mass, while the legs and feet together account for 37%. For a rough (but reasonable) calculation, we can model the arms and legs as thin uniform bars pivoting about the shoulder and hip, respectively. In a brisk walk, the arms and legs each move through an angle of about 30° (a total of 60°) from the vertical in approximately 1 second. Assume that they are held straight, rather than being bent, which is not quite true. Consider a 75-kg person walking at 5.0 km/h, having arms 70 cm long and legs 90 cm long. (a) What is the aver- age angular velocity of his arms and legs? (b) Using the average angular velocity from part (a), calculate the amount of rotational kinetic energy in this person's arms and legs as he walks. () What is the total kinetic energy due to both his forward motion and his rotation? (d) What percentage of his kinetic energy is due to the rotation of his legs and arms?