Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_247

3/247 The cart with attached x-y axes moves with an absolute speed \( v = 2 \text{ m/s} \) to the right. Simultaneously, the light arm of length \( l = 0.5 \text{ m} \) rotates about point \( B \) of the cart with angular velocity \( \dot{\theta} = 2 \text{ rad/s} \). The mass of the sphere is \( m = 3 \text{ kg} \). Determine the following quantities for the sphere when \( \theta = 0 \): \( \mathbf{G} \), \( \mathbf{G}_{\text{rel}} \), \( T \), \( T_{\text{rel}} \), \( \mathbf{H}_O \), \( (\mathbf{H}_B)_{\text{rel}} \) where the subscript “rel” indicates measurement relative to the \( x \)-\( y \) axes. Point \( O \) is an inertially fixed point coincident with point \( B \) at the instant under consideration.