Flashcards in KRSE3LEC18 Deck (27):
Angular kinetics of “uniform angular motion”
- Any force which causes a body to deviate from its straight-line path is called a “radial force”, (Fr)
- Acts perpendicular to the linear path.
For a body in curvilinear motion, the force keeping the body in the curved path
Can you give an example of a centripetal force?
Tying a string to a piece of metal and twirling it around.
The string maintains a centripetal force.
If the string is cut
the path the metal flys off at is tangential to the radius of the circle
What is the force acting on the piece of metal once the tension in the string is released?
What about “centrifugal” force?
Force that is going away from it, while centripetal is force going towards center
The object moving around the curve will have the same velocities but because they are changing direction they will have varying accelerations.
These accelerations are directed towards the center - ar
Radial Acceleration equation
ar = V^2/r
Where V is the velocity of the body & “r” the radius of the circle.
What is the formula for at ?
ar is directly proportional to
ar is inversly proportional to
- Analogous to linear force
- Fr = m x ar
Since ar = V2/r, the formula for Fr can be re-written as follows:
Fr = mV2/r
Consider this runner negotiating the curve in the track, what factors are of importance?
1. The amount of force placed on the lower extremity muscles to stay on the curved path, ie. avoid going off at a tangent to the curve.
2. The angle of lean.
When considering force: Can you list the 3 factors that would determine the force experienced on the lower extremity muscles when running around a curve?
Start with the formula.
Fr = mV2/r
- Fr is directly proportional to the mass of the runner.
- This means the heavier the runner the Greater the radial force and need to work harder
Second factor: Fr is directly proportional to the ________ of the velocity
- This means the faster the running speed the greater the radial force
Fr is inversly proportional to the radius of the curve.
- This means that the larger the radius of the track, the less radial force
The angle of lean
This is the angle at which the runner in this case has to tilt when measured from the vertical.
If AB is the force acting on the lower extremity,
what is the radial force Fr?
what is the force acting at right angles to Fr?
The radial force (Fr) is: AD - the force keeping the runner on the track.
For the angle of lean,
Tan Theta = mV2/r divided by mg
Tan Theta = V2 /rg
Therefore the angle of lean is dependent on two factors:
- The velocity of the runner.
- The radius of the curve around which the runner moves.
- This is because the other factor, gravity, will not change during the course of the performance.
first factor of the angle of lean
It is directly proportional to the square of the velocity of the runner.
Tan Theta directly proportional V2
- This means the faster the runner the angle of lean is more
second factor of the angle of lean
It is inversly proportional to the radius of the curve.
Tan Theta is directly proportional 1/r
the second factor means the greater the curve of the track the
Less the angle of lean
If F sine is equal to “mV2/r”
And F cosine is equal to “mg”
What is the angle of lean?