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Dec 8, 2017 - Chartrand, Alexander M.; McCormack, Elizabeth F.; Jacovella, Ugo; Holland, David M P; Gans, Berenger; Tang, Xiaofeng; GarcÃa,. Gustavo A.; Nahon, Laurent; and Pratt, Stephen T., "Photoelectron angular distributions from rotationally re
Problem No.2: Angular resolution. ⢠Diffraction limit: to distinguish two point objects with an instrument of aperture diametre D at wavelength λ, they must be separated by an angle larger than sin α > λ/D. Human eye. 2 mm. 500 nm. 50 arcsec. ES
Units Radians (rad), revolutions (rev) Rad/s, rev/s
“alpha”
Rad/s2, rev/s2
n/a
Sec, min, hours
t
d 1.75m = = 0.500rad R 3.5m
How far has this point traveled in degrees?
0.5rad "
!
360 o = 28.6 o 2#rad
How many revolutions has this point gone through?
S = 2πR ; θ = 360o π Rad =
Velocity Acceleration
"=
If d = R, then
180o
Angular Parameter Angular Distance (revolutions)
Example: A point on the edge of a wheel of radius 3.50 m travels 1.75 m. What is the angular distance the point traveled?
∴ 2πRad = 360o = 1 revolution
Define Radians…. Linear Distance1.
Linear Parameter Distance
0.5rad "
!
1rev = 0.0796rev 2#
!
2. Velocity – Angular Velocity (ω)
2. Velocity – Angular Velocity (ω)
! (distance) " = = t (time)
•The speed at which an object is going around in a circle. •Velocity depends on the direction.
Note that v is linear velocity
d d#1 R = vr # 1 " = R= t t R
•Direction in this case is either clockwise or counter-clockwise.
r v !" = R
!
1
3. Acceleration – Angular Acceleration
3. Acceleration – Angular Acceleration
r "v r "v 1 #! " = = R = ! t t t R
•When an object is going around in a circle faster and faster or slower and slower.
r a "# = R
•The object is changing the rate of its spin.
! Linear Eq.
v = vo + at 1
d = vot + at 2 2
v 2 =vo2 +2ad
! !
1 d = (v0 + v)t 2
Angular Eq.
" = " o + #t
1 " = # ot + $t 2 2
" 2 = " o2 + 2#$
1 " = (! o + ! )t 2
A Bicycle wheel begins rotating from rest. After 10s it has an angular velocity of 100 rad/s. What is it’s angular acceleration?
ωo = 0 ω = 100 rad/s t = 10 s α=?
ω = ωo +αt 100 = 0 + α(10) α = 10 rad/s2
! A dentist’s drill starts from rest. After 3.2 sec of constant angular acceleration it turns at a rate of 2.51x104 rev/min. Determine the angle (in radians) through which the drill rotates during this period.
2.51"10 4
ω = 2628 rad/s ωo = 0 t = 3.2 sec
A ladybug sits at the outer edge of a merry-go-round, and a gentleman bug sits near the axis of rotation. The merry-go-round makes a complete revolution every second. The gentleman bug’s angular velocity is… (Q7-1)
1. Half the ladybugs 3. Twice the ladybug’s
rev 2# rad 1 min ! ! min rev 60 s rad = 2628 s
2. The same as the ladybug’s 4. Impossible to determine.
θ = ½ (ωo + ω)t = ½ (0 + 2628)3.2 = 4205 rad
Q
2
A ladybug sits at the outer edge of a merry-go-round, and a gentleman bug sits near the axis of rotation. The merry-go-round makes a complete revolution every second. The gentleman bug’s angular velocity is… (Q7-1)
1. Half the ladybugs 3. Twice the ladybug’s
When a wheel of radius R rotates about a fixed axis as in the figure below, which of the following statements are false? A. All points on the wheel have the same angular speed.
2. The same as the ladybug’s 4. Impossible to determine.
B. All points on the wheel have the same tangential velocity C. All points on the wheel have the same angular acceleration
1. A
2. B 3. C 4. A & B 5. A & C 6. B & C
Q
When a wheel of radius R rotates about a fixed axis as in the figure below, which of the following statements are false? A. All points on the wheel have the same angular speed. B. All points on the wheel have the same tangential velocity C. All points on the wheel have the same angular acceleration