Chapter 9: Angular Kinetics
- Define moment of inertia
- How the human body's moment of inertia may be manipulated
- Newton's laws of motion as they apply to angular motion
- Define angular impulse and angular momentum
- Explain the relationship between angular impulse and angular momentum
Linear and Angular Quantities
Newton's First Law of Motion (relating to angular motion)
Angular Inertia: The property of an object to resist changes in angular motion
I = mk2
Angular inertia depends upon mass and mass distribution
Moment of inertia about eccentric axes
Ib = mk2 + mr2
Moment of inertia in a runners leg
What is the benefit to having limbs that are tapered (The proximal ends are larger than the distal ends)?
Moment of inertia in
What would be desriable in terms of bicycle wheel design (focus on inertia of the wheel I=mk2)?
Ice-skating examples of manipulating inertia (Calculation)
High Dive example
Angular Momentum in Figure Skating
Angular Momentum: H=Iω
Angular momentum in a non-rigid body can be estimated by:
H = ∑Iω
Angular momentum is conserved when no external torques are created on the body.
Angular momentum conservation requires H to be constant.
However, I and ω can change.
1. Angular momentum is conserved in which of the following activities:
2. How does "choking up" on a baseball bat affect performance?
- Gymnastics vault while in the air
- Giant swing in gymnastics
- Spin about the longitudinal axis in ice-skating
3. Does a golf club have greater angular inertia when it is held vertically or horizontally?
Newton's Second Law of Motion (relating to angular motion)
F=ma led to FΔt = mΔv
In angular motion, T=Iα leads to:
TΔt = Δ(Iω)
A change in angular momentum may result in:
True, false, or "it depends": Angular acceleration of an object indicates the presence of a net external torque.
- A change in angular velocity (volleyball serve with topspin)
- A change in direction of the axis of rotation (bicycle wheel gyroscope)
- A change in moment of inertia
Newton's Third Law of Motion (relating to angular motion)
For every torque exerted by one object on another, the other object exerts an equal torque back on the first body but in the opposite direction
Carl Lewis long jumping (video)
Crocodile death roll
How does a cat land on its feet?
How cats survive falls
High Bar Routine (story, video)