Final answer:
The torque exerted by the support bar on the gymnast's hands is 90 Nm, in accordance with Newton's third law, which states that for every action, there is an equal and opposite reaction.
Step-by-step explanation:
The question you're asking is related to Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. This law applies to the scenario of a gymnast performing a giant swing and exerting torque on a support bar. If a gymnast performs a giant swing with an angular velocity of 5 rad/sec and exerts a torque of 90 Nm on the support bar, then the support bar exerts an equal amount of torque back on the gymnast's hands. This is due to the fact that forces in nature come in pairs, and the support bar must exert a force equal in magnitude and opposite in direction, which in this case translates into torque.
Therefore, the amount of torque that the support bar exerts on the gymnast's hands is also 90 Nm. It is essential to understand that this torque plays a crucial role in the conservation of angular momentum and allows the gymnast to perform the swing correctly. This principle of equal and opposite torques is also seen in other scenarios where forces are exerted symmetrically, such as in the balance of forces on a uniform pole held by a pole vaulter or on the legs of a table evenly supporting its weight.