Shape Hollow
A space station is constructed in the shape of a hollow ring of mass 4.30 104 kg. Members of the crew walk on?
A space station is constructed in the shape of a hollow ring of mass 4.30 104 kg. Members of the crew walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius 150 m. At rest when constructed, the ring is set rotating about its axis so that the people inside experience an effective free-fall acceleration equal to g. (See figure below.) The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring.
(a) What angular momentum does the space station acquire?
(b) For what time interval must the rockets be fired if each exerts a thrust of 135 N?
I love this question 
It is truly awesome. Let's begin!
a) We need to get the space station rotating with an angular velocity ω. ω needs to be large enough so that the centripetal acceleration felt by the people walking on the inner surface of the outer wall is equal to g (9.8 m/s/s). The centripetal acceleration (lets call it a) is given by
a = v²/r
since
v/r = ω
we get
a = rω²
We want a = 9.8, thus:
rω² = 9.8.
Since the radius is 150 m we get the following value for ω:
150ω² = 9.8
ω = √(9.8 / 150) = 0.2556038602.... rad/s
This is the angular velocity at which the space station needs to be rotating at to achieve a centripetal acceleration equal to g. We want to find out what angular momentum the space station acquires. Angular momentum in general is given by:
Iω
where I = the moment of inertia and ω is the angular velocity! We have not been given a value for I, so this needs to be calculated. Since I have not been given the schematics for the space station I will have to estimate a value for I. In my estimate, I will approximate the space station by a thin ring with radius of 150m and a mass of 4.30 · 10⁴ kg. The moment of inertia for such a ring is given by the following formula:
I = mr² = (4.30 · 10⁴)(150)² = 9675 · 10⁵ kgm²
Now we can calculate the angular momentum of the space station:
Iω = (9675 · 10⁵)(0.2556038602) = 247296734.7....kgm²/s
≈ 2.473 · 10⁸ kgm²/s
So the above is the angular momentum which the space station acquires.
b)
The thrusters (rockets) blast away for t seconds exerting 135 N. t must be such that the space station acquires the angular momentum calculated above. Let us start by finding out the resulting angular acceleration caused by the thrusters.
τ = Iα
α = τ/I
where τ is the torque and α is the angular acceleration!
τ is given by
τ = r × F (be ware, this is the cross product, but since the force is perpendicular to the radius of the space station we just get)
τ = rF = (150)(135) = 20250 kgm²/s²
We already have a value for I, thus we can start calculating for the angular acceleration (alpha):
α = τ/I = (20250)/(9675 · 10⁵) = 2.093023256 · 10⁻⁵...rad/s²
Now, since we want to achieve an angular velocity of
0.2556038602.... rad/s
we need to have the rockets blasting for t seconds such that.
αt = ω
t = ω/α = 0.2556038602 / 2.093023256 · 10⁻⁵
= 12212.18443 s = 12212.18443 / (60·60) hours
= 3.392273453 hours
t ≈ 3.4 hours
I hope this helped!
Hollow Welded Roll Form Shape
 |
 Vintage Golden Collar Shape Hollow Green Resin White Crystal Pendant Necklace $7.99 Time Remaining: 25d 14h 49m Buy It Now for only: $7.99 Buy It Now |
 Fashion So Beautiful Luxurious Hollow Out Leopard Head Shape Gold Link Bracelet $4.59 Time Remaining: 1h 18m |
 Vintage Silver Vase Shape Hollow Out Blue Stone Crystal Hook Dangle Earrings $0.99 (1 Bid) Time Remaining: 3h 1m |
 1pc New fashion vintage bronze moon shape hollow stud ear cuff earrings E0462 $6.99 Time Remaining: 2d 3h 24m Buy It Now for only: $6.99 Buy It Now |
 Retro Vintage Leopard Heart Shape Hollow Carved Adjustable Ring $1.01 (3 Bids) Time Remaining: 3h 27m |
 Glitter Hollow Heart Shape Paillette Spangles for Nail Art Decoration 12 Colors $3.00 Time Remaining: 19d 4h 6m Buy It Now for only: $3.00 Buy It Now |
 12x Nail Art Plastic Hollow Star shape Decorations B16 $0.99 Time Remaining: 3h 56m |
 Fashion Copper925 Silver Electroplate Hollow Fan Shape Dangle Earrings Eardrop $3.69 Time Remaining: 4h 14m |
 Vintage Golden Chain Angel Wing Hollow Collar Shape Pendant Necklace $7.99 Time Remaining: 29d 15h 41m Buy It Now for only: $7.99 Buy It Now |
 Size 6 Hollow Leaf Shape Swarovski Crystal Finger Ring 18K White Yellow Gold GP $9.99 Time Remaining: 4h 40m |
 Bohemian Slice Leaf Shape Hollow Out Dangle Hook Fashion Earring Earrings $1.79 Time Remaining: 28d 9h 10m Buy It Now for only: $1.79 Buy It Now |
 300 pcs golden plated hollow shape and charming bead caps 6x1mm $0.06 (2 Bids) Time Remaining: 5h 44m |
 Size 6 Heart Shape Hollow Ring Topaz Clear Swarovski Crystals 18K Yellow Gold GP $7.99 Time Remaining: 7h 24m |
 Retro Vintage Leopard Heart Shape Hollow Carved Adjustable Ring $0.99 Time Remaining: 8d 2h 55m Buy It Now for only: $0.99 Buy It Now |
 Size 7 Heart Shape Hollow Ring Topaz Clear Swarovski Crystals 18K Yellow Gold GP $7.99 Time Remaining: 7h 42m |
 12 Colors Glitter Hollow Star Shape Spangles Paillette for Nail Art Decoration $3.00 Time Remaining: 26d 3h 6m Buy It Now for only: $3.00 Buy It Now |
 Size 7 Hollow Leaf Shape Swarovski Crystal Finger Ring 18K White Yellow Gold GP $9.99 Time Remaining: 7h 56m |
 5 pair tibet silver hollow ellipse drop shape dangle earring wholesale $5.99 Time Remaining: 21d 17h 47m Buy It Now for only: $5.99 Buy It Now |
 Size 8 Heart Shape Hollow Ring Topaz Clear Swarovski Crystals 18K Yellow Gold GP $7.99 Time Remaining: 8h |
 Vintage Retro Hollow Out Decorative Pattern Flower Shape Dangle Earrings $0.99 Time Remaining: 8h 46m |
 Car Vehicle Window Blk Rubber D Shape Hollow Seal Strip $13.51 Time Remaining: 27d 5h 9m Buy It Now for only: $13.51 Buy It Now |
 Tibetan Silver Hollow Water drop shape Dangle Earrings LK3 $0.99 (1 Bid) Time Remaining: 9h 13m |
 wholesale 6 pairs tibet silver hollow ellipse drop silkworm shape dangle earring $7.98 Time Remaining: 9d 4h 10m Buy It Now for only: $7.98 Buy It Now |
 Sexy Skull Shape Hollow Clubwear Min Dress XL Gray $14.99 Time Remaining: 10h 14m |
 Size6 18K Rose Gold GP Hollow Bars Shape Cocktail Ring Swarovski Crystal Arinna $9.99 Time Remaining: 11h 38m |
 New Champion Baseball STRONGEST Hollow Plastic BAT Blue Lightweight Bottle Shape $9.99 Time Remaining: 25d 14h 4m Buy It Now for only: $9.99 Buy It Now |
 Size7 18K Rose Gold GP Hollow Bars Shape Cocktail Ring Swarovski Crystal Arinna $9.99 (2 Bids) Time Remaining: 13h 30m |
 1Pair x Gold Color Double Layer Hollow Fashion Flower Shape Earring $1.45 Time Remaining: 10d 4h 16m Buy It Now for only: $1.45 Buy It Now |
 FASHION BLACK GREY SPIRAL SHAPE HOLLOW CHANDELIER LADY DANGLE EARRINGS JEWELRY $1.30 (5 Bids) Time Remaining: 14h 18m |
 ALLAHS HEART SHAPE HOLLOW CARVED PENDANT WITH 18K GOLD GP FILL 236 NECKLACE $9.99 Time Remaining: 16h 21m |
 ROMAN NUMBERS HOLLOW CIRCLE SHAPE FINGER RING SILVER PLATED FASHION JEWELRY NEW $3.99 Time Remaining: 13d 3h 36m Buy It Now for only: $3.99 Buy It Now |
 5 pieces Hollow Box Clasp Hook Bail Beads Finding Marquise Horse Eye Fish Shape $0.49 Time Remaining: 18h 9m |
 Unisex Weaving Shape Hollow Out Design Fashion Jewelry Plated Silver Ring $2.99 Time Remaining: 2d 4h 18m Buy It Now for only: $2.99 Buy It Now |
 Women Fashion Retro Hollow Carved Moon Shape Ear Pin Earring Golden FAEAR146 $0.99 Time Remaining: 20h 43m |
 A plurality of color multiple Size Round Turquoise Beads Bracelet beads $2.99 Time Remaining: 12d 13h Buy It Now for only: $2.99 Buy It Now |
 Women Fashion Retro Hollow Carved Moon Shape Ear Pin Earring Silver FAEAR146 $0.99 Time Remaining: 20h 43m |
 Stylish Hollow Fan Shape Copper925 Silver Electroplate Dangle Earrings Eardrop $3.69 Time Remaining: 22h 54m |
 ONE 925 STERLING SILVER HOLLOW TUBE BUTTERFLY SHAPE EUROPEAN STYLE BEAD $8.99 Time Remaining: 2h 53m Buy It Now for only: $8.99 Buy It Now |
 New Teenage girls Wrist watches Hours Micky Mice Shape Hollow out dial timepiece $0.01 (1 Bid) Time Remaining: 23h 25m |
 Wholesale Multicolor Multi size Turquoise Teardrop Coin Loose Bead bracelet bead $2.99 Time Remaining: 2d 8h 18m Buy It Now for only: $2.99 Buy It Now |
 Sexy Skull Shape Hollow Clubwear Min Dress XL Black $14.99 Time Remaining: 1d 24m |
 Sz7 18K Yellow Gold GP Hollow Bars Shape Cocktail Ring Swarovski Crystal Arinna $9.99 Time Remaining: 1d 28m |
 Handmade Real Wax Hollow Luminary Hurricane Shell Candle White Square Cube Shape $23.00 Time Remaining: 29d 23h 52m Buy It Now for only: $23.00 Buy It Now |
 Retro Vintage Leopard Heart Shape Hollow Carved Adjustable Ring $1.25 (4 Bids) Time Remaining: 1d 3h 27m |
 Handmade Real Wax Hollow Luminary Hurricane Shell Candle Red Square Cube Shape $23.00 Time Remaining: 29d 23h 52m Buy It Now for only: $23.00 Buy It Now |
 GOLD HEART LOVE SHAPE HOLLOW OUT LONG TASSELS HOOK DANGLE CHANDELIER EARRINGS $0.01 (1 Bid) Time Remaining: 1d 3h 48m |
 SILVER HEART LOVE SHAPE HOLLOW LONG TASSELS HOOK DANGLE CHANDELIER EARRINGS HOT $0.01 Time Remaining: 1d 5h 18m |
 BN Womens Special Shape Hollow Heel Style High Heel Bow Shoes Black Gray $14.99 Time Remaining: 10d 10h 45m Buy It Now for only: $14.99 Buy It Now |
 FASHION SILVER CHAIN HOLLOW EAR DROP U SHAPE DANGLE HOOK EARRINGS FREE SHIPPING $0.55 (2 Bids) Time Remaining: 1d 6h |
 12 Colors Hollow Star Shaped for Nail Art Decoration Free shipping B45 $3.34 Time Remaining: 13d 4h 48m Buy It Now for only: $3.34 Buy It Now |
 FASHION WOMENS MOON SHAPE HOLLOW LONG TASSEL JEWELRY LOOP HOOK DANGLE EARRINGS $0.06 (2 Bids) Time Remaining: 1d 7h 21m |
 26 x 16 MM Plain Hollow Pear Shape Sterling Silver 1" Dangle Earrings with French Wire Hook List Price: Sale Price: $10.99 You save: $17.00 (61%)  Eligible for free shipping!Availability: Usually ships in 1-2 business days See Reviews For This Product DescriptionPolish Finish .925 Sterling Silver 26 x 16 MM Wide Plain Hollow Pear Shaped Dangle Earrings.Earrings comes with French Wire hook back Finding in sterling Silver.Earrings will be shipped in FREE Gift Earrings box...  |
 Laughter Fills Our Hollow Dome Sale Price: $9.99 Eligible for free shipping!Availability: Usually ships in 1-2 business days See Reviews For This Product |
 Walnut Hollow Basswood Shapes - Basswood Shape, Round, 5 ndash; 7, 1/2 See Reviews For This Product DescriptionThese original, country woodburning shapes have the mellow, fresh-cut beauty of fine wood. Use them for découpage, decorative painting, wood carving, and woodburning. Each shape has a finely sanded, blank surface and is treated to preserve the bark. |
 Leather Hole Punch Tool, Heavy Duty List Price: Sale Price: $9.45 You save: $15.54 (62%) Eligible for free shipping!Availability: Usually ships in 24 hours See Reviews For This Product DescriptionProfessional Grade leather, synthetic or rubber hole punch with hole sizes of 5/64" , 3/32" , 7/64" , 5/32 , 1/8" , 3/16". Spring loaded handle allows you to make holes quickly and leaves a clean ready to use hole in almost any material... |
 PlanToys Mini Hollow Blocks List Price: Sale Price: $22.00 You save: $23.99 (52%) Eligible for free shipping!Availability: Usually ships in 24 hours See Reviews For This Product DescriptionA set of 15 pcs with 6 different shapes that can be played on the table encouraging group play and cooperative activity. |
 Bleach 9 Sale Price: $1.99 Eligible for free shipping!Availability: Usually ships in 1-2 business days See Reviews For This Product |
 Laughter Fills Our Hollow Dome List Price: Sale Price: $14.74 You save: $2.24 (13%) Eligible for free shipping!Availability: Usually ships in 24 hours See Reviews For This Product |
 Vermont American 1/4 inch Nut Driver - 1 quarter inch hollow shaft INDUSTRIAL . One piece hollow shaft fits the longest bolts and studs . Handle is triangle style shape for better grip. Hollow shaft accommodates bolts threads as long as 3.25 inches long this is a great tool for working on computers also. This is a unique hollow shaft tool. The Claw ... Allows nut to be placed on longer protruding List Price: Sale Price: $5.99 You save: $14.00 (70%) Eligible for free shipping!Availability: Usually ships in 1-2 business days See Reviews For This Product Description1/4" (1/4 inch) Nut driver w 3 1/3inch hollow shaft. One piece 3 1/4inch hollow shaft fits the longest bolts and studs. 1/4inch Nutdriver with one piece 3 1/4inch hollow shaft The Claw ... Allows nut to be placed on longer protruding bolt threads... |
 Novelty Gourmet Foil Wrapped Chocolate Fruit Red Apple List Price: See Reviews For This Product DescriptionEnjoy a milk chocolate foil covered apple. Hollow chocolate molded to an apple shape and then wrapped in pretty red foil wrapping. Buy in bulk and save on shipping. Great for a fruit bowl, for decoration and of course just to peel the foil off and eat right away. |
