Final answer:
To determine the speed of the center of gravity at its lowest position, calculate the potential energy at the highest position and the kinetic energy at the lowest position. The tangential speed of the free end of the rod when it reaches the vertical position can be found using the equation v = ωr.
Step-by-step explanation:
In order to determine the speed of the center of gravity at its lowest position, we need to calculate the potential energy at the highest position and the kinetic energy at the lowest position. Since the rod is initially at rest, the potential energy is equal to the gravitational potential energy, which can be calculated using the equation PE = mgh. At the highest position, the height is equal to the length of the rod, so the potential energy is PE = (0.370 kg)(9.8 m/s^2)(1.40 m). At the lowest position, the potential energy is zero, so the kinetic energy is equal to the initial potential energy. Using the equation KE = (1/2)mv^2, we can solve for the speed v: (1/2)(0.370 kg)v^2 = (0.370 kg)(9.8 m/s^2)(1.40 m). Solving for v gives us the speed of the center of gravity at its lowest position.
To calculate the tangential speed of the free end of the rod when it reaches the vertical position, we can use the equation v = ωr, where ω is the angular velocity and r is the distance from the center of rotation to the free end of the rod. At the vertical position, the distance r is equal to half the length of the rod. The angular velocity can be calculated using the equation ω = √(2gh), where h is the height from the highest position to the vertical position. Substituting the values into the equation v = ωr, we can find the tangential speed of the free end of the rod at the vertical position.