Chapter 7 - Angular Kinetics Part 2 Flashcards
(16 cards)
What is angular momentum? what is the formula?
Product of angular analog of mass (moment of inertia) times the angular analog of linear velocity (angular velocity)
*measures how much rotational motion an object has and how hard it is to stop it from spinning
Formula: L = Iw
What is the difference between moment of inertia (I) and angular momentum?
Moment of inertia: A measure of HOW much an object resist changes
Angular Momentum (L): a measure of how much rotational motion an object has
*combines moment of inertia and angular velocity
What is the formula for angular momentum?
Ha = Iaw
*refers for rotating body
Ha = angular momentum
Ia = moment of inertia
w = angular velocity
What does angular momentum depend on?
- How hard it is to rotate (inertia)
- How fast itβs rotating (angular velocity)
so,
- more mass farther from the axis > higher inertia
- spinning faster > higher angular momentum
What are examples of how athletes changes their shape of their body to change inertia and angular momentum?
A gymnast tucking during a spin
A gymnast tucking during a spin:
- reduces Ia
- increase w
- Ha stays constant if no external torque
As limbs move farther from body what happens to moment of inertia and angular velocity?
- moment of inertia increases while angular velocity decreases to keep angular momentum constant
What does a net external torque (Ta) applied to an object cause? What is the formula to that?
angular acceleration
ππ = πΌπ πΌ
Ta = net external torque
Ia = moment of inertia
a = angular acceleration
ππ = πΌπ πΌ what does this equation tell you?
If you apply a net torque to an object, it will rotate faster (gaining angular speed) unless theres no torque at all
- the more mass or the more spread out the mass (higher I), the harder it is to rotate - requiring more torqu
How does a hurdler keep its angular momentum close to zero when heβs angular velocity is high?
I=β(mi)(ri)^2
- if the mass is closer to the axis, then r is reduce which mean inertia is also reduce
- A smaller moment of inertia mean a body segment can rotate faster with less effort, which allows high angular velocity without generating excessive angular momentum
Ha = Iawβ
What is angular impulse?
the effect of torque applied over a period of time. this impulse causes a change in angular momentum
- larger torque or longer durations = larger changes in angular momentum
What can larger torques come from?
- longer moment arms
- longer time application of torque (more time to apply the force)
What is true on how torque is exerted back when a torque is exerted on an object?
For every torque exerted by one object, the other object exerts an equal torque back in the oppoiste direction
What is an external torque?
a rotational force that cause an object to rotate
Ο a = ΞHa/Ξt , what does this formula tell us?β
What are exmple?
torque is responsible for changing angular momentum.
*if you want a larger change in angular momentum (like speed up a spinning object), you need to apply a larger amount of torque or apply it over time
In diving, athletes apply torque to their bodies to change their angular momentum, helping them spin or rotate faster
What are linear and angular concepts in this chapter?
Linear:
inertia (mass)
force
Linear Momentum
Impulse
Angular:
Moment of inertia
Torque of moment of force
Angular Momentum
Angular Impulse
What are the equations, symbols, and units, for each concept in linear and angular?
Inertia = m (kg)
Force = F (N)
Linear momentum = L = mv (kg x m/s)
impulse = FdeltaT (N x s)
Moment of inertia I= Mr^2 = mk^2 (kg x m^2)
Torque of moment of force = T = F x r (Nm)
Angular Momentum = H = Iw (kg x m^2.s or Nm x s)
Angular impuse Tdelta (time) (Nm x s or kg x m^2/s)
