KINS 4200 Exam 3 Angular Kinetics II

levers definition

simple machines consisting of a relatively regic bar-like body that may be made to rotate about an axis

lever arm

the bar like body

effort arm

distance from the fulcrum to the effort force

resistance arm

distance from the fulcrum to resistance (or load) force

fulcrum

point of support or axis about which a lever may be made to rotate

mechanical advantage definition

determines mechanical effectiveness to understand which force is magnified by the lever

mechanical advantage formula

MA = effort arm / resistance arm

MA = 1

balance

MA > 1

strength

MA < 1

velocity

mechanical advantage affected by

muscle length, cross sectional area, moment arm, angle of attachment, shortening velocity, training, fatigue

1st class lever

effort force and resistance force are on opposite sides of fulcrum

optimizes balance

ex. head on spine

2nd class lever

effort force and resistance force are on the same side of the fulcrum

resistance arm < effort arm

optimizes strength

ex. lower leg

greater effort arm =

= greater torque

3rd class lever

effort force and resistance force are on the same side of fulcrum

resistance arm > effort arm

optimizes velocity (greater range of motion over time)

ex. upper arm

erector spinae

muscle group that help keep spine erect

highest torque occurs when

sitting in slouched posture

greater moment arm = greater gravitational torque

balance definition

ability of a body to assume and maintain a stable position

base of support

area bound by the outermost regions of contact between a body and support surface

stable posture =

maintain the line of gravity within the base of support

to increase stability

increase size of base of support

position COM as low as possible

increase body mass

increase friction

2nd law: law of acceleration linear

F = ma

2nd law: law of acceleration angular

T = Ia

• torque = angular acceleration x moment of inertia

moment of inertia definition

resistance of an object to angular rotation

moment of inertia formula

I = m₁r₂² + m₂r₂² + …

• r = distance of the object from the axis of rotations

angular momentum (H) =

moment of inertia (I) x angular velocity (w)

H = Iw

conservation of angular momentum

no external torque acts on object, no change of angular momentum will occur = angular momentum remains constant and is conserved

angular moment dependent on

mass, radius of rotation, angular velocity

if mass remains the same, but distance from axis of rotation differs

moment of inertia differs