Flashcards in KRSE3LEC19 Deck (30):
- The tendency to resist acceleration.
- Is directly proportional to the mass of the body.
Which of Newton’s 3 laws deals with inertia?
The Law of Inertia (Law 1)
“A body will maintain a state of rest or constant velocity unless acted on by an external force.”
The resistance to angular acceleration
- This is also a function of the mass of the body.
- Greater the mass of the body, the more difficult it is to accelerate.
Is it purely the mass of the object that we have to consider?
- In addition to the mass of the object, the distribution of this mass with respect to the axis of rotation is critical.
- This is seen when swinging bats and rackets of different weights.
- Easier to cross with pole and harder to rotate and less likely to fall off
Therefore, When considering angular motion,
the property similar to mass in linear motion, is called “moment of inertia”.
Moment of Inertia (I) equation
I = Em x r2
Moment of Inertia (I) definition
The sum of all the particles composing the object multiplied by the square of the radius of of each particle from it’s radius of rotation.
Moment of Inertia Emphasis: Because “I” is dependent on the square of the radius,
the distribution of the mass with respect to the axis of rotation is more important than the amount of mass in determining angular acceleration.
what are examples of previous explanation
- Reducing “I” when swinging a baseball bat.
- “Choking up”, pulls the bat closer to the body.
- Reduces the radius of rotation
Makes it easier to swing.
Left: how we are made,
the bigger mass are closer to the center/rotation
Determining moments of inertia
- Difficult to do in the human body … composed of irregular shapes.
- Average values for each body segment are taken using cadaver data.
- “I” is then calculated using “k” - the radius of gyration, instead of “r”.
How is “k” measured?
“k” is the distance from a given point of rotation to the mass distribution of the segments.
Angular Kinetics and Newton’s Second Law
In most situations, the most efficient way to move the human body is to maximize acceleration while minimizing torque requirements.
e.g., bend knee while running.
Angular Kinetics and Newton’s Second Law Example
If a bat is suspended by the grip and struck by a ball at the center of mass, the bat attempts to move in pure linear motion with no rotation.
- Felt as a vibration.
If the bat is struck at the center of percussion (sweet spot),
it experiences pure rotation about the suspension and no vibration is felt.
- Changes in angular momentum are normally the result of changes in the radius of rotation or changes in angular velocity.
- Changes in angular momentum are directly related to Newton’s first two laws of motion.
Angular Momentum (H)
Similar to linear momentum (mv)
H = I w
Note: Factor most dramatically influencing angular momentum is the
distribution of mass w.r.t. the axis of rotation.
flex/extend vs. pronation and supination axis of rotation
k is longer in flexion/extension than pronation/supination
**that’s why muscles are bigger, so that they can overcome a large amount of inertia
**moment of inertia when flex and extend have very long k, when pronate and supinate moment of inertia is small, therefore k is small
Conservation of Angular Momentum
- The total angular momentum of a system remains constant in the absence of external torques.
- Important in varying the rates of spin ex. Diving, ballet, gymnastics.
Angular momentum is the sum but what has changed is omega
-omega gets smaller on the right
Principle of Conservation of Angular Momentum: Ex
Example: spin of an ice skater
During a spin, the skater’s angular velocity increases as limb segments are brought closer to the body, and angular velocity decreases as the limbs are moved further from the axis of rotation.
when skating the moment of inertia is being manipulated to cause change in angular velocity.
The angular velocity changes to conserve angular momentum.
- Angular Momentum is conserved.
- Changes in “I” and “” determine the rate of spin.
Transfer of Angular Momentum
- Angular momentum can be partially transferred from one segment of the body to another in the absence of external torques.
- Make possible the initiating of twisting motions in mid-air when diving, etc.
Classic example of transferring angular momentum: cat twist
1. Cat assumes a pike: creates two axes of rotation = one for upper body and one for lower body.
2. Lower the moment of inertia for the upper body by bringing the forelimbs closer to the axis of rotation.
3. Internal torques are used to run the upper body in one direction toward the ground.
4. Cat rotates lower body toward the ground.
Linear & Angular Analogues: Mass
Mass (m)/Moment of inertia (I)
Linear & Angular Analogues: Force
Force (F)/Torque (T)
Linear & Angular Analogues: Momentum
Momentum (M)/Angular Momentum (H)