Final answer:
To find the moment of inertia of the boxer's forearm, we use the relationship between torque, moment of inertia, and angular acceleration. By calculating the torque from the force and lever arm and dividing it by the angular acceleration, we can determine the forearm's moment of inertia.
Step-by-step explanation:
To calculate the moment of inertia of the boxer's forearm, we can use the relationship between torque, moment of inertia, and angular acceleration. Torque is the product of force and the perpendicular distance from the pivot point (the effective perpendicular lever arm), and it is related to moment of inertia and angular acceleration by the formula:
\(\tau = I \cdot \alpha\)
Where:
- \(\tau\) is the torque
- \(I\) is the moment of inertia
- \(\alpha\) is the angular acceleration
To find the moment of inertia, we rearrange the formula:
\(I = \frac{\tau}{\alpha}\)
First, we convert the force of 2.00 \(\times\) 10^3 N and lever arm of 3.00 cm to torque:
\(\tau = (2.00 \(\times\) 10^3 N) \(\times\) (3.00 \(\times\) 10^{-2} m)\)
We then divide the torque by the given angular acceleration of 120 rad/s^2 to find the moment of inertia:
\(I = \frac{(2.00 \(\times\) 10^3 N \(\times\) 3.00 \(\times\) 10^{-2} m)}{120 rad/s^2}\)
Performing this calculation will give us the moment of inertia of the boxer's forearm.