Question

In: Physics

Suppose you’re eating in yet another restaurant where the dishes are shared at the table and...

Suppose you’re eating in yet another restaurant where the dishes are shared at the table and all placed uniformly on a rotating disk-like surface. Model this surface as a thin disk of radius 46.3 cm. Someone else has spun the surface, such that it is initially at an angular speed of 0.4 rev/s. The surface and food has a combined mass of 4.2 kg. The waiter, to show off, throws a new dish of dumplings (mass 0.9 kg) onto the surface at a speed of 0.7 m/s, such that the dish lands on and sticks to the very edge of the surface moving in the same direction as the rotating food. While this is happening, you quickly calculate the final angular speed of the food so that you can predict its location at any time before others have a chance to eat the dumplings. What is this speed, in rad/s?

Solutions

Expert Solution

Since there are no external torques for the system of disc and the new dish, angular momentum is conserved.

Angular momentum=I where I is moment of inertia and is angular velocity.

Also, angular momentum=mvr, where m is mass, v is velocity and r is position of the object relative to the point where angular momentum is calculated.

Moment of inertia of disc is given by: mr2/2 where m is mass and r is radius,

Moment of inertia of point mass is given by: mr2 where m is mass and r is the distance of the point mass from axis of rotation.

So, moment of inertia of disc=4.2*0.463*0.463/2 ( here, m=4.2 kg and radius =46.3 cm=0.463 m)

= 0.45 kg-m2

Initial angular velocity=0.4 rev/s=0.4*2 rad/sec=2.51 rad/s

So, initial angular momentum of disc=0.45*2.51=1.1295 kgm2/s

Initial angular momentum of the new dish=0.9*0.7*0.463 ( here m=0.9 kg,v=0.7 m/s,r=45.3 cm=0.463 m)

=0.292 kgm2/s

So,total initial angular momentum=1.1295+0.292=1.4215 kgm2/s

Final moment of inertia=moment of inertia of disc+moment of inertia of new dish=0.45+mr2=0.45+0.9*0.463*0.463

=0.643 kgm2

Let the final angular velocity be . So, final angular momentum=0.643

Initial angular momentum= final angular momentum => 0.643=1.4215 => =1.4215/0.643=2.21 rad/s


Related Solutions

Suppose you’re eating in yet another restaurant where the dishes are shared at the table and...
Suppose you’re eating in yet another restaurant where the dishes are shared at the table and all placed uniformly on a rotating disk-like surface. Model this surface as a thin disk of radius 45.3 cm. Someone else has spun the surface, such that it is initially at an angular speed of 0.4 rev/s. The surface and food has a combined mass of 3.3 kg. The waiter, to show off, throws a new dish of dumplings (mass 0.8 kg) onto the...
Suppose you’re eating in yet another restaurant where the dishes are shared at the table and...
Suppose you’re eating in yet another restaurant where the dishes are shared at the table and all placed uniformly on a rotating disk-like surface. Model this surface as a thin disk of radius 45.3 cm. Someone else has spun the surface, such that it is initially at an angular speed of 0.4 rev/s. The surface and food has a combined mass of 3.3 kg. The waiter, to show off, throws a new dish of dumplings (mass 0.8 kg) onto the...
Suppose that your favorite restaurant serves the best ramen dishes in town . Since you eat...
Suppose that your favorite restaurant serves the best ramen dishes in town . Since you eat there so often, you've observed the following : the patrons are 40% male , the probability that the patron orders a tofu-based meal given that the patron is male is 30%, while the probability that the order is tofu-based given the patron is female is 50%. One night, you walk into the restaurant and see a tofu-based dish on one of the tables that...
Brady was eating at a local restaurant that had an open fire pit. His table was...
Brady was eating at a local restaurant that had an open fire pit. His table was next to the pit. During dessert, an ember exploded out and landed on the napkin on Brady's lap, catching it on fire. Fortunately, Brady was able to get the napkin off of him before the fire burned him or his clothes. The fire was quickly put out by Brady's server. Brady was upset by the incident and sued the restaurant for ordinary negligence. What...
Question: Suppose you have organized another business under the name “PAPA’s Hotel & Restaurant” on December...
Question: Suppose you have organized another business under the name “PAPA’s Hotel & Restaurant” on December 1, 2019. In order to compete in the market, you have decided to avail of financing from Azizi Bank for further expansion. Bank requires a list of documents including financial statements for further process. The business transactions during the month of December are as follows: Dec 01: You have invested cash of $2,500,000 in your business, PAPA’s Hotel & Restaurant. Dec 01: Purchased hotel...
Suppose you’re playing a game where you consecutively roll 3 dice. After each roll you may...
Suppose you’re playing a game where you consecutively roll 3 dice. After each roll you may choose to either roll the next dice or sacrifice one die to reroll any number of the previous dice. If you get a number greater than 5 you win, but if you roll doubles or a number less than 6 you lose. Considering each roll a separate state what is the approximate branching factor? Justify. Draw the full state space considering only the number...
Suppose that a monopolistically competitive restaurant is currently serving 250 meals per day (the output where...
Suppose that a monopolistically competitive restaurant is currently serving 250 meals per day (the output where MR = MC). At that output level, ATC per meal is $10 and consumers are willing to pay $13 per meal. Instructions: Enter your answers as whole numbers. a. What is the size of this firm’s profit or loss? $. b. Will there be entry or exit? . Will this restaurant’s demand curve shift left or right . c. Assume that the allocatively efficient...
Suppose that a monopolistically competitive restaurant is currently serving 260 meals per day (the output where...
Suppose that a monopolistically competitive restaurant is currently serving 260 meals per day (the output where MR = MC). At that output level, ATC per meal is $10 and consumers are willing to pay $12 per meal. Instructions: Enter your answers as whole numbers. a. What is the size of this firm’s profit or loss? Answer:_ Will there be entry or exit?        (Click to select)   Entry   Exit      Will this restaurant’s demand curve shift left or right?        (Click to select)   Left   Right c. Suppose...
Suppose Mary goes to an all-you-can-eat Pizza restaurant. where you pay a fixed admission fee at...
Suppose Mary goes to an all-you-can-eat Pizza restaurant. where you pay a fixed admission fee at the door and then don't pay anything for any additional slices you eat. True, False or Uncertain. Justify your answer, Have to explanation why. Consider the following statement: "In the real world, we would expect that the cost of admission should have no effect on the amount of pizza consumed by a customer."
Suppose that you also had information about another blocking factor “machine”, where four machines had been...
Suppose that you also had information about another blocking factor “machine”, where four machines had been used to measure the sugar content such that each machine had been used once with each storage time and once with each storage condition i.e. the design was a Latin square design. (i) Describe the advantages/disadvantages of the Latin square design. If there are any disadvantages, explain how they may be overcome
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT