Key Equations form Movement Science:
- Moment (Torque): rotational force x moment arm of force
- Linear Displacement of a rotating segment (S): s= theta x R (radius)
o Derived from: theta= s/r
- Angular and Linear velocity: V (linear V) = w (angular V) x R (radius)
- Stress (σ) (vector- force per unit area): Pressure has the same equation as stress but the only difference is that it is a scalar. Stress = F (Newtons)/Area (m2)
- Strain (ε): quantifying amount of deformation. Usually is expressed in terms of percent, and is unit less. Strain = [(Δ Length)/(Lo)] x100 = % unitless
Δ (change), Lo (original length)
Shear Strain: same as above but just using a angle instead of length
Shear strain= ΔΘ/Θo = change in theta/ original theta
Newton’s Laws
- 1) Law of inertia: body continues to stay in uniform motion or rest unless compelled to change by a non-net zero force (change velocity).
o Angular Inertia or moment of inertia: function of mass about an axis. Object’s resistance to angular motion
§ I = mr2 (units kgm2) , r= radius of gyration
*** Radius of gyration has a much greater (exponential) impact on inertia then mass because it is squared
o Inertia: resistance to linear motion. Calculated by an objects mass in kg.
- 2) Law of Acceleration: Change in motion is proportional to the forces being imposed on the object, and motion will occur in a straight line of the net force (AKA the line of action will be a straight line).
o Sum of the F = MA (kg m/s2)
o Momentum: quantifies movement based on velocity (Speed and direction) and mass. Changes in momentum are proportional to the net force. (AKA to change momentum a net force must be applied)
§ Momentum = mv (kg m/s)
o If you divide momentum by time, it equals the net force!!!
§ mv / t = ma ***because v/t = a
o Angular Momentum:
§ Σ T (torques)= I * ω
§ Remember Inertia for angular motion = mr2, substitute this in for I in the above equation you get: Σ T (torques)= (mr2)(ω) **** So you can affect angular velocity by moving mass in and out (changing radius of gyration) around an axis of rotation (like a spinning ice skater) ****
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- 3) Law of Action and Reaction: To every action there is always opposed an equal reaction. Do not cancel each other out – they act on opposite bodies (or segments) Forces (moments) are equal .
- Momentum and Impulse Relationship: Impulse is the amount of time a force is applied, because forces are not instantaneous. Impulse is the area under the force time curve graphs.
o Rearranging equations one can see that impulse = momentum
o F x Δt (impulse)= mv (momentum) solve for F = mv/Δt à F=ma
o Can manipulate time that a force is applied to change momentum
o Angular momentum = Iω
o Angular Impulse and momentum: T (torque) * t = I * ω
EMG Calculations:
- Hertz (sample rate): number of samples obtained in a second (60 hz= 60 samples per second)
- Sampling frequency: 1/hz (Example: you have a device that is set to take 60 pictures per second or at 60hz. If you divide 1/60= .017 (this means you have to take a sample every .017 second in order to achieve 60 samples per second) ***In general you want to have a sampling rate that 2-10 times greater then the frequency (.017/10)= .0017 (your sampling rate always has to be smaller then the frequency you are trying to capture)