A uniform, solid sphere of radius 3.75 cm and mass 2.50 kg starts with a purely translational speed of 1.00 m/s at the top of an inclined plane. The surface of the incline is 1.00 m long, and is tilted at an angle of 34.0' with respect to the horizontal. Assuming the sphere rolls without slipping down the incline, calculate the sphere's final translational speed v2 at the bottom of the ramp. U2 = m/sA trapeze artist performs an aerial maneuver. While in a tucked position, as shown in Figure A, she rotates about her center of mass at a rate of wj = 6.03 rad/s. Her moment of inertia about this axis is I; = 17.3 kg.m. A short time later, the aerialist is in the straight position, as shown in Figure B. If the moment of inertia about her center of mass in this position is now If = 33.7 kg.m, what is her rotational speed of ? Figure A Of = rad/s & TOOLS x10The spaceship Intergalactica lands on the surface of the uninhabited Pink Planet, which orbits a rather average star in the distant Garbanzo Galaxy. A scouting party sets out to explore. The party's leader-a physicist, naturally-immediately makes a determination of the acceleration due to gravity on the Pink Planet's surface by means of a simple pendulum of length 1.45 m. She sets the pendulum swinging, and her collaborators carefully count 108 complete cycles of oscillation during 206 s. What is the result? acceleration due to gravity: m/s2