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Physics I Class 14

Rotational Motion

Definitions of angular position q angular velocity

angular acceleration

Relationship between variables in angular motion and linear motion

Rotational inertia (or moment of inertia I )

Rotational kinetic energy K

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Definitions

Angular Position: q (always in radians) Angular Displacement:

Angular velocity:

lim

t0

qt

dqd t

(Previously we only considered cases with constant .) Angular acceleration:

lim

t0

t

dd t

d2q

d t 2

0 0 (You pick for each problem.)q q q q

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Analogy BetweenLinear and Rotational Variables

(more about torque later)

Uniform Circular Motion (review)

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r

a=ac

Δq

ac v2

r

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Angular Displacement and Angular Velocity

• Use your right hand.• Curl your fingers in the direction of

rotation.• Thumb points in the direction of

increasing q and angular velocity . v r

• Mathematically:cross product of two vectors,

Review

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1D Equations of Motion for Constant Acceleration a.

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Equations for Constant

All equations are written for q in radians. Sometimes you will need to convert radians to/from degrees or revolutions.

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Finite size rigid objects are collections of infinitely small point-like elements

s q r

v r

| atangential | r

| ar || ac |v2

r2 r2

r2 r

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Rotational inertia & Energy

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Torque causes rotation

Torque and angular acceleration are always in the same direction.

Massless rodm

tF

r

Axis of rotation

Newton's Second Law appliesFor rotation about a fixed axis:

Ft ma

rFt mra mr(r) mr2

Torque : rFt I

r F I

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Take-Away Concepts

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Problems of the Day

1. A cyclist is riding his bicycle due east in the Tour de France bicycle race. What is the direction of the angular velocity of his bicycle wheels?

A) North. B) South. C) East. D) West. E) Up. F) Down.

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Problems of the Day

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Answer of problem of the day

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Activity 14 Rotational MotionGoal: Study the relation between linear and rotational variables

Apparatus: Labpro, a power supply, use digital channel 2, two masses (each 0.050 kg), a rod LoggerPro, open rotation.xmbl

Analysis: Part A and part B

0.12 m

0.06 m

Procedures:

1) Separation of two masses r= 0.06 m (Measure r to the center of each mass.)

Start rotation with period about 1 sec. Measure angular velocity as function of time and acceleration .

2) Separation of two masses r= 0.12 m

Start rotation with period about 1 sec.Measure angular velocity as function of time and acceleration .

Analyze data for t < 20 sec.