Final answer:
Dynamic muscular actions performed at a constant angular limb velocity are called isotonic exercises, typically involving concentric or eccentric contractions during weight lifting. Calculations of angular acceleration and work done in these exercises require an understanding of torque, force, lever arms, and moment of inertia.
Step-by-step explanation:
The dynamic muscular actions that are performed at a constant angular limb velocity are known as isotonic exercises. These exercises involve moving limbs against resistance, such as lifting weights, where the muscles change length during the movement, performing either concentric contraction (muscle shortening) or eccentric contraction (muscle lengthening).
Example of Angular Acceleration:
Consider an example where a woman is working out to develop muscle tone. As she flexes her arm, lifting a 2.00-kg weight, we can calculate the angular acceleration with the given data:
- Force exerted by biceps: 750 N
- Distance from elbow to weight: 24.0 cm
- Moment of inertia of forearm: 0.250 kg·m²
- Effective perpendicular lever arm: 2.00 cm
To determine the angular acceleration, we use the formula:
α = τ/I
τ = r × F
where α is the angular acceleration, τ is the torque, F is the force applied, r is the lever arm, and I is the moment of inertia of the limb.
Example of Work Done:
To calculate the work done, we use the formula:
W = τ × θ
where W is the work done, τ is the torque, and θ is the angle in radians through which the force is applied.In this case, if the woman flexes her arm through an angle of 60.0°, we first convert this angle to radians and then calculate the work done using the torque we have already computed.