Macmillan The forearm of length Larm = 35.2 cm shown in the figure is positioned at an angle with respect to the upper arm, and a 3.30-kg ball is held in the hand. The total mass motal of the forearm and hand is 2.80 kg, and their center of mass is located at LCM = 14.2 cm from the elbow. The biceps muscle attaches to the forearm at a distance Lbiceps = 4.0 cm from the elbow. What is the magnitude of the force Fbiceps that the biceps muscle exerts on the forearm for 0 = 63°?
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
![**Text Description:**
The forearm of length \( L_{\text{arm}} = 35.2 \, \text{cm} \) shown in the figure is positioned at an angle \( \theta \) with respect to the upper arm, and a \( 3.30 \, \text{kg} \) ball is held in the hand. The total mass \( m_{\text{total}} \) of the forearm and hand is \( 2.80 \, \text{kg} \), and their center of mass is located at \( L_{\text{cm}} = 14.2 \, \text{cm} \) from the elbow. The biceps muscle attaches to the forearm at a distance \( L_{\text{biceps}} = 4.0 \, \text{cm} \) from the elbow.
**Questions:**
1. What is the magnitude of the force \( F_{\text{biceps}} \) that the biceps muscle exerts on the forearm for \( \theta = 63^\circ \)?
\[
F_{\text{biceps}} = \quad \text{N}
\]
2. What is the magnitude of the force \( F_{\text{joint}} \) that the forearm exerts on the elbow joint for \( \theta = 63^\circ \)?
\[
F_{\text{joint}} = \quad \text{N}
\]
**Image Diagram Explanation:**
The diagram on the right shows a simplified anatomical representation of the arm, focusing on the forces and distances involved in holding a ball. It displays:
- An arm bent at the elbow holding a ball.
- The length of the arm (forearm with hand), \( L_{\text{arm}} \).
- The biceps muscle and its attachment point on the forearm.
- The angle \( \theta \) between the forearm and upper arm.
- Distances from the elbow to key points: the center of mass (\( L_{\text{cm}} \)) and the biceps attachment (\( L_{\text{biceps}} \)).
The illustration helps in visualizing the mechanical advantage and torques around the elbow joint due to the muscle force and the weight of the ball.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4551f2ef-4c78-4d27-9320-7cb594875026%2Fe59f375b-8aac-4bdb-980c-c5f9b8d17d3f%2Fmgxij8s_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
