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Torque and Rotational Motion Torque and Rotational Motion

Torque and Rotational Motion - PowerPoint Presentation

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Torque and Rotational Motion - PPT Presentation

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

torque angular practice rotational angular torque rotational practice force vector physics net videos problem radians mass units rotation momentum

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Slide1

Torque and Rotational Motion

HTHS AP Physics 1M. DimlerSlide2
Slide3

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)Slide19
Slide20

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 vSlide33
Slide34

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.