2 centripetal acceleration problems

• kcskcskcsyes
In summary, the conversation discusses the concept of using rotating cylinders as colonies in space and determining the necessary angular speed for the cylinder to have equal centripetal acceleration and Earth's free-fall acceleration at its surface. The second part involves an air puck suspended on a string and revolving on a frictionless table, with questions about tension, horizontal force, and speed. The use of the formula a=v^2/r is mentioned as a possible solution for the first problem.
kcskcskcsyes
Any help would be greatly appreciated...

It has been suggested that rotating cylinders about 10 mi long and 5.0 mi in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth?

An air puch of mass 0.25 kg is tied to a string and allowed to revolve in a circle of radius 1.0 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of 1.0 kg is tied to it. The suspended mass remains in equilibrium while the puck on the tabletop revolves. a) What is the tension in the string? b) What is the horizontal force acting on the puck? c) What is the speed of the puck?

First, you need to show us what you've attempted so far on these problems. What formulas do you know?

um i think on the first one you use the a=v2/r equation
is that correct?

1. What is centripetal acceleration?

Centripetal acceleration is the acceleration that an object experiences as it moves along a curved path. It is always directed towards the center of the circular path and is responsible for keeping the object in its circular motion.

2. How do you calculate centripetal acceleration?

Centripetal acceleration can be calculated using the formula a = v²/r, where a is the centripetal acceleration, v is the linear velocity of the object, and r is the radius of the circular path.

3. What is the difference between centripetal and centrifugal force?

Centripetal force is the force that acts towards the center of the circular path, while centrifugal force is the perceived outward force experienced by an object in circular motion. Centrifugal force is not a real force, but rather a result of the object's inertia.

4. Can centripetal acceleration change?

Yes, centripetal acceleration can change if the linear velocity or radius of the circular path changes. It is directly proportional to the square of the velocity and inversely proportional to the radius, so any changes in these values will result in a change in centripetal acceleration.

5. What are some real-life examples of centripetal acceleration?

Some real-life examples of centripetal acceleration include a car going around a curve, a spinning top, a roller coaster, and the rotation of planets around the sun. Essentially, any object that moves along a curved path experiences centripetal acceleration.

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