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Biomechanics Sec. 4

The document summarizes key concepts in biomechanics including: 1) The center of mass and center of gravity are the points where mass is evenly distributed or gravity is balanced, respectively. 2) Newton's laws of motion describe how forces affect the motion of objects. An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. 3) Impulse is equal to change in momentum, and torque is equal to the product of moment of inertia and angular acceleration based on Newton's second law.

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86 views23 pages

Biomechanics Sec. 4

The document summarizes key concepts in biomechanics including: 1) The center of mass and center of gravity are the points where mass is evenly distributed or gravity is balanced, respectively. 2) Newton's laws of motion describe how forces affect the motion of objects. An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. 3) Impulse is equal to change in momentum, and torque is equal to the product of moment of inertia and angular acceleration based on Newton's second law.

Uploaded by

omar alsade
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Biomechanics

Sec. 4
COM & COG
• The center of mass: is the point which its mass is evenly distributed in
all directions.
• The center of gravity: is the point about which the effects of gravity
are completely balanced.
Newton’s first law: law of inertia
Newton’s first law states that a body remains at rest or at a constant linear
velocity except when compelled by an external force to change its state.
• Inertia:
the amount of energy required to alter the velocity of a body.
• The mass moment of inertia of a body:
It is a quantity that indicates its resistance to a change in angular velocity.
• Mass moment of inertia (𝐼) = 𝐾𝑔. 𝑚2 = (𝑀 × 𝐿2 )
• Law of “Conservation of angular momentum”: If the body's mass moment
of the inertia decreased, the angular velocity will increase.
Whiplash injury
Static Equilibrium Vs. Dynamic Equilibrium
• A body is in static equilibrium when its linear and rotational
velocities are zero, the body is not moving.

• The body is in dynamic equilibrium when its linear or


rotational velocity is not zero, but is constant.
NEWTON’S SECOND LAW: LAW OF ACCELERATION

• Newton′ s second law of linear motion: σ 𝐹 = 𝑚. 𝑎


•𝐹∝𝑎
•𝐹∝𝑚
1
•𝑚∝
𝑎
• Work = W = 𝐹. 𝑑
𝑤𝑜𝑟𝑘 (𝑊)
• Power = P =
𝑡𝑖𝑚𝑒 𝑇
• If σ 𝐹 = 0, 𝑎 = 0 and the body in a linear equilibrium.
• If the net force produces acceleration, the body will accelerate in the
direction of the resultant force.
Newton’s second law of rotary motion
• The angular acceleration of the rotating forearm is proportional to the
internal torque, but is inversely proportional to the mass moment of
inertia.
• Ex: the Elbow joint.
• σ 𝑇 = 𝐼. α
Impulse-Momentum Relationship
∆𝑣
• 𝐹 = 𝑚. 𝑎. 𝑎=
𝑡

• ∴ 𝐹. 𝑡 = 𝑚. ∆𝑣 (linear impulse-momentum relationship.)

• Momentum describes the quantity of motion possessed by a body.

• Impulse is a force applied over a period of time.

• 𝑇. 𝑡 = 𝐼. ∆ω 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑖𝑚𝑝𝑢𝑙𝑠𝑒 − 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑠ℎ𝑖𝑝


Work-energy Relationship.
• Linear work: the product of the magnitude of the force (F) applied
against an object and the linear displacement of the object in the
direction of the applied force.
• 𝑊 = 𝐹. 𝑑 "𝑁/𝑚 = 𝐽"
• Angular work: the product of the magnitude of the torque (T) applied
against an object and the angular displacement of the object in the
direction of the applied force.
• 𝑊 = 𝑇. 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 "𝑁/𝑟𝑎𝑑 = 𝐽"
• Concentric activation of the biceps brachii produces positive work.

• Eccentric activation of the biceps brachii produces negative work.

• Isometric activation of the biceps brachii no work produced.


Power
• Power (P) is work (W) divided by time.
𝑊
•𝑃= 𝑊 = 𝐹. 𝑑
𝑡
• ∴ 𝑃 = 𝐹 × 𝑣. 𝐼𝑛𝑠𝑡𝑎𝑛𝑡𝑎𝑛𝑒𝑜𝑢𝑠 𝑝𝑜𝑤𝑒𝑟 , 𝑂𝑟 𝑇 × ω.

• Positive power reflects the rate of work done by concentrically active


muscles against an external load.
• Negative power, in contrast, reflects the rate of work done by the
external load against eccentrically active muscles.
NEWTON’S THIRD LAW: LAW OF ACTION-
REACTION

• Every action has an equal and opposite reaction.


• Ground reaction force (GRF).

• Anthropometry: the measurement of certain physical design features


of the human body.
Free Body Diagram
• The free body diagram is a simplified sketch that represents the
interaction between a body and its environment.

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