Question

The force produced by a muscle would have maximum rotatory component and least amount of dislocating or stabilising component at what angle of attachment to the bone?

• A. 60 degrees
• B. 45 degrees
• C. 90 degrees
• D. 0 degrees

Hint:

At \(90^\circ\): - \(\sin \theta = 1\) → Maximum rotation - \(\cos \theta = 0\) → No stabilizing/dislocating force So, 90° is the most efficient angle for movement.

Answer 1

The Correct Option is C

Concept:
When a muscle exerts force on a bone, the force can be resolved into two components:
• Rotatory Component: Perpendicular to the bone; responsible for movement (rotation).
• Parallel Component: Along the bone; may cause either:
• Stabilizing force (towards joint), or
• Dislocating force (away from joint) The effectiveness of movement depends on maximizing the rotatory component and minimizing the parallel component.

Step 1: Resolving force into components.
If a force \(F\) acts at an angle \(\theta\) to the bone: \[ \text{Rotatory Component} = F \sin \theta \] \[ \text{Parallel Component} = F \cos \theta \]

Step 2: Condition for maximum rotation.
The rotatory component is maximum when: \[ \sin \theta = 1 \] This occurs at: \[ \theta = 90^\circ \]

Step 3: Condition for minimum parallel component.
The parallel component becomes: \[ F \cos 90^\circ = 0 \] Thus, at \(90^\circ\), there is:
• No stabilizing force
• No dislocating force

Step 4: Interpretation.
At \(90^\circ\), the entire muscle force contributes to rotation, making movement most efficient.

Step 5: Final conclusion.
Therefore, the angle at which:
• Rotatory component is maximum
• Parallel component is minimum is: \[ \boxed{90^\circ} \]