111 Torque Increased Force Increased Torque Increased Radius Increased Torque 111 Torque Only the tangential component of force causes a torque 111 Torque This leads to a more general definition of torque ID: 494151
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Slide1
Chapter 11 – Rotational Dynamics & Static EquilibriumSlide2
11.1 - Torque
Increased Force = Increased Torque
Increased Radius = Increased TorqueSlide3
11.1 -
Torque
Only the tangential component of force causes a torque:Slide4
11-1 Torque
This leads to a more general definition of torque:
**********r is also referred to as the “moment arm”************Slide5
Question 11.1
Using a Wrench
You are using a wrench to loosen a rusty nut. Which arrangement will be the most effective in loosening the nut?
a
c
d
b
e)
all are equally effectiveSlide6
11.1 - Torque
Is torque a vector?
YES! Why?
Because FORCE is a vector!
What is the torque direction?If the torque in question causes
Counterclockwise
(CCW) angular acceleration
Torque is
positive
.
Clockwise
(CW) angular acceleration
Torque is negative.Slide7
11.1 - Torque
The Right Hand Rule in Physics
Coordinate systems
Moving charges in magnetic fields
Magnetic fields produced by currentTorqueAngular MomentumSlide8
11.1 - Torque
Right Hand Rule for Torque
Make a “backwards c” with your right hand.
Turn hand so your fingers curl in the direction of rotation that particular torque would cause.
Direction of thumb dictates “direction” of torque.
Positive torque points out of the page.
Negative torque points into the page.
http://electron9.phys.utk.edu/Collisions/rotational_motiondetails.htmSlide9
11.2 - Torque & Angular Acceleration
Linear Dynamics
Newtons’s
Second Law for Linear Dynamics:
Reads if we apply a FORCE to an object with some
mass
, the object undergoes an
acceleration.
Rotational Dynamics
Newton’s Second Law for Rotational Dynamics:
Reads, if we apply a TORQUE to some object with
some moment of inertia
, the object undergoes an
angular acceleration
.Slide10
Newton’s Second Law
Linear
Rotational
Force
Mass
Acceleration
Torque
Moment of Inertia
Angular AccelerationSlide11
A person holds his outstretched arm at rest in a horizontal position. The mass of the arm is
m
, and its length is .740 m. When the person allows their arm to drop freely, it begins to rotate about the shoulder joint. Find (
a
) the initial angular acceleration of the arm, and (b) the initial linear acceleration of the hand. Slide12
(
a
)
α
= ?(b
) a = ?
Notice anything interesting about the acceleration of the hand?Slide13
11.2 – Torque & Angular Acceleration
We found that the acceleration of the hand was:
a= (3/2)g
This means for points on the arm > (2/3)L away from the axle have an acceleration 1.5g!!Slide14
11.3 – Static Equilibrium
Static Equilibrium occurs when
An object has no translational motion.
AND
An object has no rotational motion.Conditions for static equilibrium.
Net force in the x-direction is zero.
Net force in the y-direction is zero.
Net torque is zero.Slide15
11.3 - Static
Equilibrium
If the net torque is zero, it doesn’t matter which axis we consider rotation to be around; we are free to choose the one that makes our calculations easiest.Slide16Slide17
11.3 - Static
Equilibrium
When forces have both vertical and horizontal components, in order to be in equilibrium an object must have no net torque, and no net force in either the
x
- or
y
-direction.Slide18Slide19
11-4 Center of Mass and Balance
If an extended object is to be balanced, it must be supported through its center of mass.Slide20
11-4 Center of Mass and Balance
This fact can be used to find the center of mass of an object – suspend it from different axes and trace a vertical line. The center of mass is where the lines meet.Slide21
11-5 Dynamic Applications of Torque
When dealing with systems that have both rotating parts and translating parts, we must be careful to account for all forces and torques correctly.Slide22
11.6 – Angular Momentum
Linear Momentum
An object with
mass (m)
moving linearly at velocity (v) has a certain amount of
linear momentum (p).
Angular Momentum
A rotating object with
moment of inertia (I)
rotating at some
angular velocity (
ω
)
has a certain amount of
angular momentum (L)
.Slide23
11.6 -
Angular Momentum
Using a bit of algebra, we find for a particle moving in a circle of radius
r
,Slide24
11.6 – Angular Momentum
Linear Momentum
We were able to relate the linear momentum of an object to the linear version of Newton’s Second Law.
Angular Momentum
We can do the same by relating the angular momentum of an object to the rotational version of Newton’s Second Law.Slide25
11.7 – Conservation of Angular Momentum
Linear Momentum
If the net
external
force on a system is
zero
, the
linear momentum is conserved
.
Angular Momentum
If the net
external
torque
on a system is
zero
, the
angular momentum is conserved.Slide26
11.8 – Rotational Power & Work
Linear Work
A
force
acting through a distance does work on an object to move it.
Rotational Work
A
torque
acting through an
angular displacement
does work on an object to rotate it.Slide27
11-8 Rotational Work and Power
Power is the rate at which work is done, for rotational motion as well as for translational motion.
Again, note the analogy to the linear form: