Momentum, Gravity & Equilibrium

Resolution of forces Any vector that is directed at an angle can be considered to have two parts Horizontal part Vertical part

Here the single force can be resolved in to two components Vertical component shows the force on the dog upwards Horizontal component shows the force on the dog rightwards

Calculate the vertical and horizontal vector components in the following examples Which component will make this cart move, horizontal or vertical ?

Calculate the resultant force A single force that can be applied instead of several forces

Momentum A quantity expressing the motion of a body or system, equal to the product of the mass of a body and its velocity Vector quantity Divided as Linear momentum & Angular momentum

Linear Momentum P = m v P = Momentum Momentum is frame dependant M = Mass V = Velocity Momentum is frame dependant in this ex. A is the reference compared to that the apple has a V1 velocity What can you say about the next picture ?

Angular Momentum Object fixed to a relative fixed point L= IW L = Angular momentum I = Inertia W = Angular velocity Describe as the rotational analog of the linear momentum

Physiotherapy Applications

Action and reaction To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts

State the place of reaction acting in the following action forces

Friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. Types of Friction Fluid friction Lubricated friction Skin friction

Reducing Friction Devices Wheels, ball bearings, roller bearings, many thermoplastic materials ( nylon ) Physiotherapy application Quadriplegic patients immobile for long period of time very porn for pressure sores. We apply water filled bad between the contacting surface and the bed.

Physiotherapy applications Lubricants Oil, water, grease Physiotherapy applications Mainly reduces the skin friction In manipulative techniques as effleurage, stroking to reduce the skin friction we use talc/powder When ultra sound treatments are given to provide a medium we use gel When giving nerve stimulation to minimize the skin resistance we wet the electrode pads with water

Rotation and pivot Three dimensional objects rotates either around an imaginary axis (rotational axis) or around a point (pivot point) Speed of the rotation is given by angular velocity

What is angular velocity? Vector quantity Velocity depends on the torque acting on the system AV = Degrees/time Units given by radius per second

Angular velocity Linear velocity Vector Rotation around a fixed axis Velocity depends on the torque Velocity of a system or a group of objects V= r w Vector Not around a fixed axis Depends on external forces Velocity of a single object

Angle of pull of a muscle The angle between the line of pull and the portion of mechanical axis between the point of application and the joint

Force may be resolved into a vertical and a horizontal component Size of each depends on angle of pull A muscle’s angle of pull changes with every degree of joint motion So do the horizontal & vertical components The larger the angle (00 - 900), the greater the vertical and less the horizontal components

Most resting muscles have an angle of pull < 900 Angle of pull ctd Vertical component is perpendicular to the lever, and is called the rotary component (aka angular force or movement force) Horizontal component is parallel to the lever, and is called the nonrotary component (aka stabilizing force) Most resting muscles have an angle of pull < 900

Rotary vs Nonrotary components Angle of pull < 900 As the angle of pull gets smaller, the moment arm decreases. Nonrotary force is directed toward fulcrum Stabilizing effect Helps maintain integrity of the joint Almost all of the force generated is directed back to the joint, pulling the bones together

Angle of pull > 900 Nonrotary force is directed away fulcrum Dislocating component It is called a dislocating force because the force generated is directed away from the joint Muscle is at limit of shortening range and does not exert much force

Angle of pull = 900 Force is all rotary/angular force The moment arm is at its greatest length Angle of pull = 450 Rotary & nonrotary components are equal Muscular force functions: Movement Stabilization

Gravity Natural phenomenon by which physical bodies attract with a force proportional to their mass Earth is surrounded by its own gravitational force The strength of the gravitational field is numerically equal to the acceleration of objects under its influence value at the Earth's surface 9.81 m/s2

W = mg When an object is falling under the influence of gravity Its acceleration equals to the gravitational field Weight of an object on the earth is taken as, W = mg W = weight m = mass of the object g = gravitational field

Center of Gravity (COG) Balance point, weight on all sides equal Average location of the weight of an object How do you determine the COG in a equal shape object? How do you determine the COG in irregular shape object ?

Line of Gravity Vertical line that passes through COG Represents the direction gravity acts on the body

Equilibrium State of Equilibrium All forces acting on an object are balanced Base of Support (BOS) Part of body/object in contact with supporting surface Has different shapes, according to the contact surface More the base of support increases more the stability of an object

What can you say about the shapes of following BOS

BOS in physiotherapy Patients need a support to increase there functional independence. Patients with fractures Elderly patients Muscular imbalances

Aids use in physiotherapy to increase BOS and support

States of Equilibrium Stable Unstable Neutral COG must be raised in order to disturb object Unstable Only slight force needed to disturb Neutral Object disturbed but no change in COG (ball)