HTHS AP Physics 1 M Dimler Torque Torque is a force that causes an object to turn Torque Force directed perpendicular to the lever arm of an object that has the ability to rotate the object around a fulcrum or axis ID: 656673
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Slide1
Torque and Rotational Motion
HTHS AP Physics 1M. DimlerSlide2Slide3
Torque
Torque is a force that causes an object to turnTorque
- Force directed perpendicular to the “lever arm” of an object that has the ability to rotate the object around a fulcrum or axis.
Note: this is usually an easy distance to visualize
τ = FdUnits of Torque are the Newton-MeterSlide4
Direction of the Torque Vector
The Torque vector is perpendicular to both the
position
vector and the
force
vectorRight Hand Rule: point fingers of your right hand in the direction of r vector (lever arm from center of rotation), and bend your fingers in the direction of the force vector. Your thumb then points in the direction the torque vector.Positive torques cause ccw rotation,
negative torques cause cw rotation.Slide5
Net Torque
When a force is not exactly acting perpendicular to the “lever arm”, it needs to be broken down into x and y components.Slide6
Net TorqueSlide7
Equilibrium
Static Equilibrium implies that the net force and the net torque are zero, and the system is at rest.
Dynamic Equilibrium
implies that the net force and the net torque are zero, and the system is moving at constant translational and rotational velocity
Rotational Equilibrium
implies that the net torque on an object is zero.Slide8
Radians and Degrees
Once around a circle = 360° = 2π
radians = 1 revolution = 1 rotationSlide9
Rotational Kinematics
Angular Position Symbol (θ)
Units (radians)
Formula (
θ
=s/r)s=θrAngular DisplacementSymbol (Δθ)Units (
radians/s)Formula (
Δθ=θ2-θ1
)Slide10
Practice Problem
A disk can rotate about its central axis like a merry-go-round. Which of the following pairs of values for its initial and final angular positions, respectively, give a negative angular displacement:
-3 rad,+5 rad
-3 rad, -7 rad
7 rad, -3 radSlide11
Rotational Kinematics
Angular VelocitySymbol (ω
)
Units (
radians/sec)
Formula (ω=Δθ/Δt)v=ω
rNote: Same at any point along disk
Angular AccelerationSymbol (α)Units (
radians/sec
2
)
Formula
(
α
=
Δω
/
Δ
t
)
a
t
=
α
r and
a
r
=v2/r=ω2rSlide12
Practice Problem
Find the magnitude of the earth’s angular velocity in radians per second. Then determine the linear speed of an object on the surface of the earth.Slide13
Practice Problem
A bear rides a unicycle. If the unicycle wheel begins at rest, and accelerates uniformly in a ccw direction to an angular velocity of 15 rpms in a time of 6 seconds, find the angular acceleration of the unicycle wheel.Slide14
Practice Problem
What is the average angular velocity in the first two seconds?
What is the angular acceleration at 4 seconds?
What is the angular displacement during the 10 second interval?Slide15
AP Physics 1 MC Practice ProblemSlide16
Center of MassSlide17
Moment of Inertia
Derivation of I for a point mass
½mv
2
= ½I
ω2v=ωr½ m(ωr)2
= ½Iω2
½ mω2r2 = ½I
ω
2
m
r
2
= I
Note: Units of I are kg∙m
2Slide18
Moment of Inertia
(Rotational equivalent to mass)Slide19Slide20
Moments of Inertia can be added together to find the Moment of Inertia of a system consisting of two or more objects.
∑I = I1
+ I
2Slide21
AP Physics I MC PracticeSlide22
AP Physics I MC PracticeSlide23
Newton’s 2nd Law for RotationSlide24
Sample Problem
A 20-kg ladder of length 8m sits against a frictionless wall at an angle of 60°. The ladder just barely keeps from slipping.
Draw a FBD of the ladder.
Determine the force of friction of the floor on the ladder.
Determine the coefficient of friction between the ladder and the floor.Slide25
AP MC Practice ProblemSlide26
AP Physics I MC PracticeSlide27
Toilet Paper Roll DropSlide28
Parallel Axis TheoremSlide29
Rotational Kinetic EnergySlide30
Conservation of EnergySlide31
Angular Momentum
Angular Momentum is a measure of how difficult it is to stop an object when rotating. Units of Angular
Momentum:
kg∙m
2
/sSlide32
Angular Momentum
The angular
m
omentum of a point mass can be found by multiplying the linear momentum of the point mass (p=m
x
v) by the perpendicular distance from axis of rotation to the point mass (r).
L = r x m x vSlide33Slide34
Conservation of Angular MomentumSlide35
Angular ImpulseSlide36
Bozeman Science Videos
http://www.bozemanscience.com/ap-physics
Click on the link above and watch the following videos.
Torque
Rotational Motion
Angular MomentumVector Properties of Angular QuantitiesAngular ImpulseConservation of Angular MomentumRotational InertiaSlide37
Aplusphysics.com Video Lessons
http://www.aplusphysics.com/courses/ap-1/AP1_Physics.html#ap1
Click on the link above and watch the following videos.
Rotational Kinematics
Torque
Rotational DynamicsAngular MomentumRotational Kinetic EnergySlide38
Twu Videos
https://www.youtube.com/playlist?list=PLUn4SDRnHn7cpTOIptsleLOSwhj4as8vm
There are 52 videos on the Rotational Motion playlist. They are relatively short videos, so you should watch all 52 videos prior to next Unit test. You will be quizzed twice a week to ensure you are pacing yourself.