Week 9 - Angular Kinetics Torque Flashcards
Define torque
Tendency of a force to cause rotation, the turning effect produced by a force
Torque equation
𝜏 = F * MA
OR
𝜏 = F * d
𝜏 = torque (Nm)
F = applied force (N)
MA or d = moment arm (m)
What type of force is this?
Concentric force acting on the axis of rotation causing translation of the object
What type of force is this?
An eccentric force acting outside the axis of rotation resulting in translation of the object and a clockwise torque
What is a force couple
A pair of forces which are equal in magnitude, parallel and opposite in direction
Define Intertia
Inertia is the law of universal laziness. Objects want to keep doing what they are already doing.
Angular inertia depends on two things
Mass of the body AND how the mass is distributed with respect to the axis
Define moment of inertia and what is the formula?
Sum of all mass particles multiplied by the radius squared
𝐼 = 𝑚𝑟2
I = moment of inertia (measured in kilogram metres squared (kg.m2 ))
m = sum of all particles masses (measured in kilograms (kg))
r = radius of gyration (m)
Define RADIUS OF GYRATION (K)
Distance from the axis of rotation to a point where the body’s mass could be concentrated without altering its rotational characteristics (maximum mass located)
Which bat is harder to swing and why?
Moment of intertia = mass x distance of mass from moment arm
The radius is the same, although the right bat has a greater mass
Which bat will be harder to swing? and why?
They both have the same COM although the right is further to the axis, therefore being harder to swing
Which person will have the greatest moment of inertia and why?
The one of the left, as the radius of the limbs is greater than the other three
Why does a tightrope walker use a pole? 3 reasons
- Increased weight = greater inertia = increased linear stability
- Lower centre of mass = increased angular stability
- Increased moment of intertia = increased resistance to rotation
Newton’s first law for linear motion
A body will remain at rest or in constant motion unless acted upon by a net external force
Newtons first law for angular motion
A rotating body will continue in a state of rest or constant angular moment unless acted upon by a net external torque
ΣT = 0
Newton’s second law for angular motion
The rate of change of angular momentum of a body is proportional to the torque causing it AND the change takes place in the direction in which the torque acts.
ΣT = Iα
Newton’s third law in angular motion
For every torque exerted by body A to body B, an equal and opposite torque is exerted by body B onto body A
ΣTA to B = -ΣTB to A
Equation for angular momentum
𝑳 = 𝑰w
𝑳 = angular momentum
𝑰 = moment of inertia
w = angular velocity
Consider a rotating body of 10kg for which the radius is 0.2m and the angular velocity is 3 rad/s.
What is the Angular Momentum?
𝑳 = 𝑰w
𝑳 = 𝑰w
L = (10 x 0.2squared) x 3
L = 1.2 kg.m2/s
What causes a greater angular momentum? Increases the mass or radius?
Radius
Doubling the mass or velocity will double the angular momentum.
Doubling the radius, will quadruple the angular momentum.
Conservation of Momentum
Any given system will continue to move with constant linear (translatory motion) or angular (rotating about an axis) momentum unless an external force (linear) or torque (angular) acts on the system to change the momentum
If a diver doing a front roll decreases the moment of inertia what happens to the angular velocity?
It increases
If a diver increases the moment of inertia what happens to angular momentum?
It decreases
Impulse linear equation
Impulse = Ft
Ft = m(vf - vi)
Impulse angular equation
impulse angular = T*t (torque x time)
T*t = I(wf - wi)
