Final Joke Flashcards
Angular Inertia
Property of an object to resist changes in angular motion
What affects Angular Inertia
- the mass of an object
* the distribution of mass of an object relative to the axis of rotation.
Moment of Inertia
- Quantification of Angular Intertia
-Can be distributed among multiple axis of rotation
• an object is composed of many particles of matter all with a certain mass. Each particle resists motion. The greater the distance that particles are located away from the axis of rotation the harder it is to rotate.
Moment of Inertia Equation
I = mk2
This equation states that moment of inertia (I) is dependent on the mass of the object (m) and the distance from the mass to the axis of rotation (k).
• This equation shows that distribution of mass (k) has a greater
influence on angular inertia than mass (m) does
The Radius of Gyration (K)
The length measurement that represents the concentrated mass of the object from the axis of rotation…well not quite…
Really just think of k as the term quantifying the distribution of mass
Angular Momentum
L = Iw
Angular momentum is defined as the tendency for an object to remain in angular motion.
• Angular momentum (L) is determined by the moment of inertia of an object and it’s angular velocity (w).
If the Moment of Inertia Changes, what happens to the Angular Velocity
If the moment of inertia changes, the angular velocity of the object will change to maintain the same momentum.
Newton’s Second Law as it pertains to angular kinetics
If a net external force is exerted on an object at a
distance from the axis of rotation, the object will
accelerate angularly in the direction of the net external
torque, and its angular acceleration will be proportional
to the net external torque and inversely proportional to
its moment of inertia.
Angular Impulse
Angular Impulse is a measure of a torque applied for a
certain amount of time
Angular Impulse = Torque X time
J = Mt
• The net torque acting over some interval of time will cause a change in angular momentum of an object.
ex) • A diver must maximize the time that the force can
be applied by having a large moment of inertia but
then quickly minimize the moment of inertia to
increase his angular velocity.
Work
• Work is the product of force and the displacement in the direction of that force.
U = Fd
- U is the work done on an object
- F is the force applied to the object
- d is the displacement of the object in the line of action of the force.
- The unit of measurement is a joule or ft.lb or N.m (=joule)
- If you move an object a certain distance you have done work on that object
What Happens When a Weight Lifter lifts weights
• But what if the weightlifter lifts the weight and then lowers the weight.
• The displacement will be zero.
• The work will also be zero, even though the
weightlifter definitely expended energy.
• There was physiological work done
by the lifter however, there was no
overall mechanical work because the
weight is in the same position.
Positive and Negative Work
• Positive work is done when a force displaces an object in the same direction as the
force. = Concentric muscle contractions
• For example a pitcher does positive work against a baseball when throwing it.
- Negative work is done when the object is displaced in the direction opposite the force = Eccentric Muscle Contractions
- For example, the weightlifter lowering the weight
Energy and its two types
- Energy is the capacity (or ability) to do work.
- Heat, light, sound, chemical, mechanical.
- Kinetic energy
- Potential energy.
Kinetic Energy
Due to motion
• if one object, in motion, hits another object, the moving object does work on the second object and vice versa.
KE = ½ mv2
• The units are kg m2/s2 which is the same as N.m so the units are
the same as work.
• Determining kinetic energy is easier than determining work because we can measure mass and velocity a lot easier than measuring force.
Potential Energy
Due to position
- Potential energy comes in two forms;
- Gravitational potential energy
- Which is energy due to the position of an object relative to the earth
- Strain energy
- Which is energy due to the deformation of an object.
Gravitational Potential Energy
• This energy is related to the weight of an object and its elevation or height above the ground or some reference.
- PE = mgh Or PE = Wh (W for weight)
- The units for gravitational potential energy are N.m (joules)
Strain Energy
Related to an objects stiffness, its material properties and its deformation
• strain energy in the deformed pole in pole vault.
• In the board in spring board.
- The greater the deformation of the object the greater the strain energy.
- There is energy being stored in the deformed object
SE = 1/2kx2
• k is the spring constant or stiffness constant of the material normally
measured in N/m
• x is the amount of deformation
Energy Conservation
• The law of conservation of energy states that the total amount of energy in a system remains constant (“is conserved”), although energy within the system can be changed from one form to another or transferred from one object to another.
Pole Vaulting with energy
- As the pole vaulter runs toward the bar, he gains kinetic energy.
- As he bends the pole, he does work on the pole and stores elastic potential energy in the pole.
- The stored elastic potential energy is converted into gravitational potential energy as the pole does work on the pole vaulter to lift them high above the ground.
Work - Energy Relationship
Essentially if we exert work on an object horizontally the work will be converted into kinetic energy and accelerate the object until another external force acts on the object to produce a negative work
Power
• Power is the rate of doing work
P = U/t
or
P = Fv.
Power is described as the ability to exert a force over a distance in a certain amount of time. Power can be considered how fast or slow work is done.
• The units of power are watts or joules/s another unit of power is
horsepower.
Remember moving books with Power
Do you • Move all the books at once. • High force, low velocity Or • Move the books one at a time • Low force, high velocity Or • something in between.
Power in Muscles
- As contraction velocity increases our ability to produce force decreases
- As contraction velocity decreases our ability to produce force increases.
- Think about trying to lift light and heavy weights at the gym
- It is easy to lift a light weight quickly but not a heavy weight.
- This best choice would be at a medium force and a medium velocity.
- On average the maximum power output occurs at a velocity of approximately 35-60% of the muscles maximum contraction velocity.
Two Types of Fluid Forces
A buoyant force
• Due to immersion in fluid
A dynamic force
• Due to relative movement in fluid
• Lift force
• Drag force
Buoyant Force
• An object submerged in water will experience • pressure from the weight of the water above • Pressure from the water beside • Pressure from the water below to hold up the object and the water above the object
Rlower-Rupper = buoyant force
• As you submerge an object
deeper and deeper in water the
force (pressure) above and the force (pressure) below increase. The pressure below the submerged object will always be greater than the pressure above.
Archimedes Principle
- The difference between the force above and force below will always be related to the weight of the volume of fluid displaced
- So the buoyant force will always be acting up on the object and will be related to the weight of the fluid displaced
Results of the Buoyant Force
If buoyant force = mg, object will be in static equilibrium
• If buoyant force > mg, object will accelerate upwards
• If buoyant force < mg, object will accelerate downwards
What happens if we submerge an object with the same volume and mass as the fluid displaced?
- Then the buoyant force will equal the force of gravity of the object and the object will be in static equilibrium
- mg=buoyant force
What happens if we submerge an object with the same volume but a higher mass as the fluid displaced
Then the buoyant force will be less than the force of gravity and the object will accelerate downward.
• mg>buoyant force
What happens if we submerge an object with the same volume but lower mass as the fluid displaced
Then the buoyant force will be greater than the force of gravity and the object will accelerate upward.
• mg