2F 2F 2m 2r m 2r 2m 1 3 4 FIGURE P7.19

A diver leaves the platform with her body straight. Her body is in a relatively slow rotation, with an angular speed of 4.0 rad/s. She then tucks into a pike position, with her body essentially folded in half. We can use a simple model to understand what happens next. First, model her 50 kg,1.8 m body as uniform. Next, assume that when she goes into a pike position, shown in (Figure 1), she really does fold her body exactly in half. In terms of this model, what is her angular speed in the pike position? Express your answer in radians per second.   In terms of this model, how many rotations does she complete in the 1.3 s that she holds the pike position? Express your answer as a number of rotations.   Intial moment of intertia = 14   pike position inertia= 3.4

Can you show me how to solve this?

a.) A tension force, T, of magnitude 5.0 N is applied to the end of a bar at a distance r = 1.5 m from the axis of rotation O (represented by the black dot). The angle between the force and the distance vector, θ=25o. Calculate the magnitude and direction of the torque vector.   b.) In the previous problem, let’s make some changes.  The bar is now a different length and reoriented within 3-D space such that the r is a vector that has components (3,2,0) in the xyz coordinate frame, and F is a vector with components (4,5,0). What is the torque exerted on the rigid body about a pivot located at the origin? Express your answer in i, j, k, components.  Assume all distances are represented in meters and forces in newtons.