KIN 311 I A - Test 3

Define torque, moment arm, center of gravity, base of support, and stability.

Torque = turning effect of a force

Torque (moment of force) is the turning effect produced by a force.

Torque can change angular motion or help maintain equilibrium.

Muscles create torque about joints.

The relevant moment arm is perpendicular to the force line of action.

Moment arm = perpendicular distance

Shortest distance between the force line of action and the axis of rotation.

Longer moment arm → larger turning effect.

Shorter moment arm → smaller turning effect.

Do not confuse moment arm with the full length of a limb or implement.

Center of gravity (CG)

•Point in a body or system where the entire mass may be assumed to be concentrate

•cg is an imaginary point in space

•Not a physical entity

•Not a fixed point

•Changes when parts of an object change position

 

•The force of gravity acts downward through the cg

 

•Center of gravity is the point of balance

CG = point used to represent the body's mass for gravitational analysis

Base of support

Wider base → more room for the CG projection before it reaches the edge.

Narrow base → less room for error.

One-foot stance dramatically reduces the base of support.

Sport examples: defensive stance, single-leg landing, skating, gymnastics, and pitching balance.

Stability = resistance to loss of equilibrium

•A body is more stable when the CG remains within the base of support.

•Important factors: CG height, base of support, mass, and friction.

•Lower CG + wider base generally increases resistance to tipping.

•Sport stability is dynamic—not just a stationary stance.

Difference between centric and eccentric forces

•Centric force

•Force line of action directed through center of gravity

•Causes changes in translation only

 

•Eccentric force

•Force line of action not directed through center of gravity

•Causes changes in translation and rotation

Calculate torque using force and perpendicular moment arm.

Torque = force x perpendicular momentum arm

T = Torque (n*m)

F = Force (N)

r = momentum arm (m)

Longer moment arm →

larger turning effect (torque).

The door handle is far from the hinges, so the moment arm is longer. A smaller force is needed to produce the same torque (open the door).

Shorter moment arm →

smaller turning effect (torque).

The door handle is close to the hinges, so the moment arm is shorter. A larger force is needed to produce the same torque (open the door).

Calculate net torque using appropriate positive and negative signs.

Torques around the same axis can be added and subtracted

 

•Net torque is calculated by summing torques

•ΣT = Tclockwise (-) + Tcounterclockwise (+)

•ΣT = Tinternal(-) + Texternal(+)

Explain how body position affects CG and stability.

CG location depends on the position of each limb

cg height: 55% (female) to 57% (male) of standing height

Lift left arm away from side: cg shifts to the left

 

•Lift left arm in front of body: cg shifts forward

 

•Raise both arms away from side: cg shifts upward

A body is more stable when the CG remains within the base of support.

•Important factors: CG height, base of support, mass, and friction.

•Lower CG + wider base generally increases resistance to tipping.

•Sport stability is dynamic—not just a stationary stance.

Distinguish absolute and relative angular position.

•Absolute angular position

•One line or plane is fixed and immovable relative to the earth

•Orientation of a body part to the horizontal or vertical

•Relative angular position

•Both lines or planes are capable of moving

•Joint angle: angle between two body segments

Explain relationship between linear and angular velocity

•Points farther from an axis of rotation travel greater linear path than points closer to an axis of rotation at the same time

•Farther: greater distance (and greater displacement)

 

•Points farther from an axis of rotation travel at a greater linear speed (and greater instantaneous linear velocity) than points closer to an axis of rotation

Mathematically, ℓ = △⍬r

•Where

•ℓ = arc length (distance travelled, in meters)

•△⍬ = angular displacement (must be in radians)

•r = radius (distance from axis of rotation, in meters)

Calculate angular displacement, angular velocity, and angular acceleration.

Angular displacement = △⍬ = ⍬f − ⍬i

Angular velocity = Δ⍬/Δt

Angular acceleration = wf-wi/Δt

Distinguish tangential acceleration from centripetal acceleration.

Tangential Acceleration

•Component of linear acceleration tangential to circular path

 

•Mathematically: aT = ⍺r

 

•Where

•aT  = instantaneous tangential acceleration

•⍺ = instantaneous angular acceleration (must be in rad/s2)

•r = radius

Centripetal (Radial) Acceleration

•Centripetal acceleration: acceleration directed toward the axis of rotation (center of the circular path)

•Caused by the centripetal force (towards the center of the path)

 

•Two equations for ar

•One related to vT

•One related to ⍵

•Expressed as related to angular velocity (⍵)

 

•Mathematically: ar = r⍵

 

•Where

•ar = instantaneous centripetal acceleration

•r = radius

•⍵ = angular velocity (must be in rad/s)

Calculate moment of inertia for a point mass.

Radius of gyration: makes it easier to calculate I

 

•Mathematically, Ia = mka2

 

Where

•Ia = moment of inertia about axis a through the cg

•m = mass of the object (kg)

•ka = radius of gyration about axis a through the cg (m)

Distribution has a greater effect, as seen by Ia = mka2

 

•Double the mass = 2 × I (double)

•Double the radius of gyration (k) = 4 × I (quadruple)

Explain the relationship between moment of inertia and angular velocity.

•Mass farther from the axis creates more angular resistance

•Mass closer to the axis creates less angular resistance