Law of Inertia

What is Newton’s First Law of Motion?

A body at rest remains at rest and a body in motion remains in motion, in a straight line at the same velocity, until acted upon by an unbalanced force.

What is Inertia?

Resistance to a change in the state of linear motion.

What are the Inertial and Motion factors for Linear and Angular motion?

Linear: Inertial factor = Mass (m), Motion factor = Linear Velocity (v).

Angular: Inertial factor = Moment of Inertia (I), Motion factor = Angular Velocity (w).

How is Mass calculated, and what are its standard units?

Mass = weight/gravity (m=wt/g). Units are kilograms or slugs (lb*sec²/ft)

What is the formula for Linear Momentum ($M$)?

M = mv (Mass * Velocity).

How does momentum affect the force required to change an object's motion?

Greater momentum requires more force to increase/decrease velocity or change direction; less momentum requires less force.

What is the formula for Angular Momentum (L)?

L = Iw(Moment of Inertia * Angular Velocity)

What is Moment of Inertia ($I$) and its formula?

Resistance of an object/lever to change its rotational/angular motion. Formula: I = mk²

What is the radius of gyration ($k$) and why is it important?

k is the distance from the Axis of Rotation (AoR) to the point representing the concentration of mass. Because k is squared in $I = mk², where mass is concentrated is more important than the amount of mass

Why does a figure skater spin faster when pulling their arms in?

Pulling arms close to the body decreases k, which drastically decreases Moment of Inertia (I). Since angular momentum ($L = Iw) is conserved, Angular Velocity (w) must increase.

Why do sprinters flex their knee during the leg recovery phase?

Flexing the knee brings the mass of the leg closer to the hip joint (axis of rotation), decreasing k and I. This makes the leg easier to swing forward quickly with less muscle torque

What is Newton’s Second Law and its linear formula?

Law of Acceleration: The application of force causes an acceleration of the mass. Formula: F = ma

If equal force is applied to a small mass and a large mass, which accelerates more?

The object with the small mass will accelerate more

What is the angular equation for Newton’s 2nd Law?

r = Ia (Torque = Moment of Inertia * Angular Acceleration). In the human body: Muscle Torque (E=MAe) = Inertia of segments/implements (I) * Movement acceleration (a)

What is the Impulse-Momentum equation?

Ft = m(vf - vi) or Ft = mvf - mvi. Impulse (Ft) equals the change in momentum.

How do you reduce impact force ($F$) when landing from a jump or catching a ball?

Increase the time of force application (t) by flexing joints (knees, hips, elbows). Increasing t decreases the peak force F needed to stop the momentum

How does increasing time ($t$) increase the velocity of a thrown object?

Increasing the time an accelerating force is applied (Ft) increases the total change in momentum, resulting in higher final velocity (vf). (e.g., long wind-up in pitching, crow-hop, longer backswing)

What is the Law of Conservation of Momentum?

In a closed system, momentum remains constant unless acted upon by an external unbalanced force. Formula: (m1 v1i + m2 v2i) = (m1 v{1f} + m2 v2f)

What is Newton’s Third Law of Motion?

For every action there is an equal (magnitude) and opposite (direction) reaction. (For every force exerted, an equal and opposite force is exerted back)

Give an example of Ground Reaction Force in movement

When jumping or pushing off blocks, feet exert force downward and backward against the ground/block; the ground exerts an equal and opposite force upward and forward on the athlete

Why does a rifle recoil backward slowly while the bullet accelerates forward rapidly?

Equal forces are applied to both. The bullet has a very small mass, resulting in high acceleration; the rifle + shooter has a large mass, resulting in low acceleration

What is the angular application of Newton’s Third Law?

For every torque exerted by one body segment, there is an equal and opposite torque exerted on another segment around a common Axis of Rotation

How does Torque – Counter Torque apply in the Long Jump airborne phase?

Rotating the legs in one direction creates an equal and opposite counter-torque in the upper body/arms to control body rotation in mid-air.

How does Torque – Counter Torque apply in the Fosbury Flop?

Arching/extending the trunk over the bar causes the legs to move down; snapping hips upward forces the head/shoulders down to clear the bar

What is inverse dynamics in biomechanics research?

Mathematical calculations used to estimate the amount of force absorbed at human joints