0
A ferris wheel with a radius of 12 m makes one complete rotation every 8 seconds. what is the magnitude of their centripetal acceleration?
Wiki User
∙ 11y ago
5.3m/s^2
Wiki User
∙ 11y ago
Add your answer:
Earn +20 pts
What is meant by centrifugal force?
A fictitious force caused by rotation - it feels as if a force pushes you towards the outside. The magnitude of the ficticious acceleration is equal to the real centripetal acceleration: a = v2/r. The corresponding force can be obtained from Newton's Second Law.
Why would orbiting space stations that simulate gravity likely be large structures?
Artifical gravity is created by the outward acceleration (centrifugal force) as an object rotates around an axis of rotation. The magnitude of this outward acceleration is given by the centripetal acceleration, which is the opposing inward acceleration keeping the rotating object in circular orbit around the rotating object. In space, this would be done by rotating a space station until the centripetal acceleration is equal to the acceleration of gravity on Earth. Centripetal acceleration is given by the equation: Centripetal Acceleration = Velocity2/ Radius. As you can see, the magnitude of the centripetal acceleration is largely dependent upon the object's distance (distance) from the axis of rotation. Thus, in a space station that is fairly small (has a small radius), a standing astronaut will feel a different centripetal acceleration in his head than in his feet. Take the example of an astronaut standing up in a circular rotating space station with radius 5m and rotating at a speed of 7 m/s. At the astronauts feet (about 5 meters from the axis of rotation), the astronaut's centripetal acceleration will be given by the following equation. CA = 72/5 --> CA = 9.8 m/s2. This is roughly equal to Earth's gravitation acceleration. Now, lets see the magnitude of centripetal acceleration at the astronauts head. If the astronaut is 6 feet tall (about 1.83 meters), then the radius of rotation at the astronauts head is only 3.17 meters (5 meters - 1.83 meters). The speed of rotation will also be slower because the astronauts head, being closer to the axis of rotation, will have to complete a relatively smaller circle to complete one rotation in the same amount of time as the feet. After calculations, the resulting speed of rotation is 4.289 m/s rather than 7m/s. Thus, the centripetal acceleration at the astronauts head is given by the following equation: CA = 4.2892/3.17 --> CA=5.803 m/s2. Thus, we see a serious inconsistency between the centripetal acceleration at the feet of the astronaut and at the head of the astronaut (9.8 m/s2 at the feet and 5.803 m/s2 at the head). This difference would make the astronaut feel extremely uncomfortable and nauseated, rendering them unable to function at the high level needed for space. Instead, lets look at a large space station design. Take, for example, the Stanford Torus, a design that consists of a large 1.8 km in diameter rotating ring. At this large size, the space station would only need to rotate at one rotation per minute and at a rotating speed of 94.24 m/s in order to simulate Earth's gravitational acceleration. with a radius of 900m, the 1.83 meter difference between a astronaut's feet and head would be negligible and thus an astronaut would feel just as if he or she were on Earth. This is why space stations that intend to simulate gravity should be built large enough to minimize the significance of the difference between the radius of rotation of one's feet and one's head.
What is Newton's law for rigid rotation?
( t = I a ) Rotational motion and centripetal acceleration. This is defined by its equations of motion.
How is the radius of rotation related to the centripetal force and angular velocity?
Assuming that angles are measured in radians, and angular velocity in radians per second (this simplifies formulae): Radius of rotation is unrelated to angular velocity. Linear velocity = angular velocity x radius Centripetal acceleration = velocity squared / radius Centripetal acceleration = (angular velocity) squared x radius Centripetal force = mass x acceleration = mass x (angular velocity) squared x radius
Can centripetal force produce rotation?
no, but rotation can produce centripetal force
How does the centripetal force with the speed of rotation of the body with constant mass and radius of rotation?
You can calculate the centripetal ACCELERATION with one of these formulae: acceleration = velocity squared / radius acceleration = omega squared x radius Acceleration refers to the magnitude of the acceleration; the direction is towards the center. Omega is the angular speed, in radians per second. To get the centripetal FORCE, you can use Newton's Second Law. In other words, just multiply the acceleration by the mass.
What is meant by centrifugal force?
A fictitious force caused by rotation - it feels as if a force pushes you towards the outside. The magnitude of the ficticious acceleration is equal to the real centripetal acceleration: a = v2/r. The corresponding force can be obtained from Newton's Second Law.
Why would orbiting space stations that simulate gravity likely be large structures?
Artifical gravity is created by the outward acceleration (centrifugal force) as an object rotates around an axis of rotation. The magnitude of this outward acceleration is given by the centripetal acceleration, which is the opposing inward acceleration keeping the rotating object in circular orbit around the rotating object. In space, this would be done by rotating a space station until the centripetal acceleration is equal to the acceleration of gravity on Earth. Centripetal acceleration is given by the equation: Centripetal Acceleration = Velocity2/ Radius. As you can see, the magnitude of the centripetal acceleration is largely dependent upon the object's distance (distance) from the axis of rotation. Thus, in a space station that is fairly small (has a small radius), a standing astronaut will feel a different centripetal acceleration in his head than in his feet. Take the example of an astronaut standing up in a circular rotating space station with radius 5m and rotating at a speed of 7 m/s. At the astronauts feet (about 5 meters from the axis of rotation), the astronaut's centripetal acceleration will be given by the following equation. CA = 72/5 --> CA = 9.8 m/s2. This is roughly equal to Earth's gravitation acceleration. Now, lets see the magnitude of centripetal acceleration at the astronauts head. If the astronaut is 6 feet tall (about 1.83 meters), then the radius of rotation at the astronauts head is only 3.17 meters (5 meters - 1.83 meters). The speed of rotation will also be slower because the astronauts head, being closer to the axis of rotation, will have to complete a relatively smaller circle to complete one rotation in the same amount of time as the feet. After calculations, the resulting speed of rotation is 4.289 m/s rather than 7m/s. Thus, the centripetal acceleration at the astronauts head is given by the following equation: CA = 4.2892/3.17 --> CA=5.803 m/s2. Thus, we see a serious inconsistency between the centripetal acceleration at the feet of the astronaut and at the head of the astronaut (9.8 m/s2 at the feet and 5.803 m/s2 at the head). This difference would make the astronaut feel extremely uncomfortable and nauseated, rendering them unable to function at the high level needed for space. Instead, lets look at a large space station design. Take, for example, the Stanford Torus, a design that consists of a large 1.8 km in diameter rotating ring. At this large size, the space station would only need to rotate at one rotation per minute and at a rotating speed of 94.24 m/s in order to simulate Earth's gravitational acceleration. with a radius of 900m, the 1.83 meter difference between a astronaut's feet and head would be negligible and thus an astronaut would feel just as if he or she were on Earth. This is why space stations that intend to simulate gravity should be built large enough to minimize the significance of the difference between the radius of rotation of one's feet and one's head.
What is Newton's law for rigid rotation?
( t = I a ) Rotational motion and centripetal acceleration. This is defined by its equations of motion.
When the speed of rotation of a space station were doubled the centripetal acceleration o the astronaut would be?
In the simplest case, supposing the orbit of the space station to be a perfect circle, the centripetal acceleration would be quadrupled (F=mω2r).
How is the radius of rotation related to the centripetal force and angular velocity?
Assuming that angles are measured in radians, and angular velocity in radians per second (this simplifies formulae): Radius of rotation is unrelated to angular velocity. Linear velocity = angular velocity x radius Centripetal acceleration = velocity squared / radius Centripetal acceleration = (angular velocity) squared x radius Centripetal force = mass x acceleration = mass x (angular velocity) squared x radius
Can centripetal force produce rotation?
no, but rotation can produce centripetal force
What is uniform circular motion?
Uniform circular motion describes motion in which an object moves with constant speed along a circular path.In physics, uniform circular motion describes the motion of a body traversing a circular path at constant speed. The distance of the body from the axis of rotation remains constant at all times. Though the body's speed is constant, its velocity is not constant: velocity, a vector quantity, depends on both the body's speed and its direction of travel. This changing velocity indicates the presence of an acceleration; this centripetal acceleration is of constant magnitude and directed at all times towards the axis of rotation. This acceleration is, in turn, produced by a centripetal force which is also constant in magnitude and directed towards the axis of rotation.
What is the force that keeps an object moving on a curved path that is directed inward toward the center of rotation?
Centripetal force works opposite tangential acceleration.
If the magnitude of applied force falls short of required centripetal force then the object will move away from the centre of the circle?
Yes. It would spiral away such that the radius of rotation will increase, until the radius is large enough for the centripetal force to decrease to the applied force. (Centripetal force= mv2/r)
Centripetal force can it produce rotation?
A centripetal force is, by definition, a force that makes a body follow a curved path. So, yes, a centripetal force causes rotation about a point in space.
If a car turns right can acceleration be zero?
No, any turning object undergoes acceleration because the direction is always changing. The acceleration vector points into the circle of rotation, and the velocity vector is a tangent line to the circle at any given point. The equation is Centripetal Acceleration=v^2/r
