Biomechanics Notes

Time

SI unit: s (second), always convert to seconds.

Unit Conversion

1 inch (in) = 0.0254 meters (m) = 2.54 centimeters (cm)
1 kilogram (kg) = 2.2 pounds (lbs)
1 foot (ft) = 0.3048 m
1 yard (yd) = 3 ft
1 ft = 12 in
1 mile (mi) = 1.609 kilometers (km)

Basic Dimensions & Units of Measurement

Mass

• Measure of inertia, representing the amount of matter in an object.

• SI unit: kg (kilogram).

• Mass is often confused with weight but is distinct; mass does not change irrespective of location.

• 1 kg = 1,000 grams (g) and 1 kg = 2.2 pounds, which helps in understanding mass in imperial units.

Weight

• Measure of the force of gravity acting on an object with units in Newton (N).

• Weight depends on mass and the acceleration due to gravity.

• $N = 9.81 \frac{m}{s^2}$, indicating the force of gravity on Earth.

• Weight can be calculated using the formula: $Weight = m \times g$ where g = 9.81 m/s².

• Units for weight are always given in Newtons (N), and this concept is pivotal in physics calculations.

Velocity (v)

• Defined as the distance traveled over a unit of time, showcasing both speed and direction.

• It can be represented mathematically as:
  $v = \frac{distance}{time \ interval}$
  $v = \frac{change \ in \ position}{change \ in \ time}$
  $v = \frac{\Delta p}{\Delta t}$
  $v = \frac{p2 - p1}{t2 - t1}$

• Unit: m/s, indicating meters per second, a standard unit in kinematics.

Introduction to Biomechanics

• Biomechanics merges biology and mechanics, focusing on the study of forces and their effects on living organisms.

• Primarily revolves around humans in the context of exercise and sports performance.

• Why Biomechanics?

  • Enhance skill performance by understanding what works and why it works.

  • Reduce the risk of injury through analysis of movement patterns.

  • Improve overall technique, equipment, and training protocols based on biomechanical analysis.

Additional Measurements

Basic Dimensions & Units of Measurement (Length)

• SI unit: meter (m), fundamental for measurements involving length.

• 1 m = 3.28 ft or 39 inches to facilitate conversions between metric and imperial systems.

• 1 km = 1,000 m, supporting large distance calculations.

More Units of Measurement

Acceleration (a)

• Defined as the change in velocity divided by the change in time, outlining how quickly an object is speeding up or slowing down.

• $a = \frac{\Delta v}{\Delta t}$

• Unit of acceleration is $\frac{m/s}{s} = \frac{m}{s^2}$. This delineation is vital in understanding motion dynamics.

• Example: $1 \frac{m}{s^2}$ signifies that for every second, the velocity increases by 1 m/s.

Practice Problems

1. 
   $v = \frac{d}{\Delta t} = \frac{400 \ m}{20 \ s} = 20 \frac{m}{s}$

2. Runner: A runner starts from rest and reaches a velocity of 16 m/s in 8 seconds. Determine the acceleration during this interval.
   $a = \frac{\Delta v}{\Delta t} = \frac{16 \frac{m}{s}}{8 \ s} = 2 \frac{m}{s^2}$

Assignment #1 Chapter 0

• Include all relevant equations, document all work, and ensure correct units are applied.

• Round to two decimal places during all calculations.

• Provide clear, thorough explanations and details to support findings.

Key Concepts

3. Mass: Measure of inertia, reflecting how much matter is present in an object (unit: kg).

4. Weight: Measure of gravitational force acting on an object (unit: N).

5. Velocity: Distance per unit of time (unit: m/s).

6. Application Problem: An athlete runs from the 40-m line to the 70-m line in 3 seconds.
   $v = \frac{70-40}{3} \frac{m}{s} = 10 \frac{m}{s}$

7. Application Problem: A cyclist covers 50 m in 10 seconds. Determine the velocity and calculate distance for 30 minutes at that speed.
   $v = 5 \frac{m}{s}$

8. Acceleration: Change in velocity over change in time (unit: $\frac{m}{s^2}$).

Additional Example

• A runner from a dead start achieves a velocity of 8 m/s after 4 seconds. What is their acceleration in this time frame?
  $a= 2 \frac{m}{s^2}$

Force

• Defined in Newtons (N), this is a physical quantity