8. Centripetal Forces & Gravitation

Uniform Circular Motion

Obtaining an expression for angular velocity and a formula for angle as a function of time.

A ball travels on a frictionless circular track at 3m/s. The ball cannot have an acceleration greater than 1.5m/s2 or it will go off the track. What is the smallest radius the circular track can have so that the ball stays on the track?

Anderson Video - Uniform Circular Motion

Intro to Circular Motion

The earth has a radius of 6380 km and turns around once on its axis in 24 h. (b) If arad at the equator is greater than g, objects will fly off the earth’s surface and into space. (We will see the reason for this in Chapter 5.) What would the period of the earth’s rotation have to be for this to occur?

At its Ames Research Center, NASA uses its large “20-G” centrifuge to test the effects of very large accelerations (“hypergravity”) on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and an astronaut is strapped in at the other end. Suppose that he is aligned along the centrifuge’s arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this device is typically 12.5g. (a) How fast must the astronaut’s head be moving to experience this maximum acceleration?

At its Ames Research Center, NASA uses its large “20-G” centrifuge to test the effects of very large accelerations (“hypergravity”) on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and an astronaut is strapped in at the other end. Suppose that he is aligned along the centrifuge’s arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this device is typically 12.5g. (b) What is the difference between the acceleration of his head and feet if the astronaut is 2.00 m tall?

The radius of the earth’s very nearly circular orbit around the sun is 1.5 x 10^11m. Find the magnitude of the earth’s (a) velocity

The 10 mg bead in FIGURE  CP8.69 is free to slide on a frictionless wire loop. The loop rotates about a vertical axis with angular velocity ω. If ω is less than some critical value ω꜀, the bead sits at the bottom of the spinning loop. When ω > ω꜀, the bead moves out to some angle θ. a. What is ω꜀ in rpm for the loop shown in the figure?<img src="https://lightcat-files.s3.amazonaws.com/problem_images/eb6589c29b2128d4-1677611783081.jpg" alt="" />

A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min. (b) What is the radial acceleration of the blade tip expressed as a multiple of g?

A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min. (a) What is the linear speed of the blade tip, in m/s?

Uniform Circular Motion - IB Physics

The radius of the earth’s very nearly circular orbit around the sun is 1.5 x 10^11m. Find the magnitude of the earth’s (b) angular velocity

Relating linear and angular speed in physics.

A 200 g block on a 50-cm-long string swings in a circle on a horizontal, frictionless table at 75 rpm. (a) What is the speed of the block?

The earth has a radius of 6380 km and turns around once on its axis in 24 h. (a) What is the radial acceleration of an object at the earth’s equator? Give your answer in m/s2 and as a fraction of g.

Uniform Circular Motion and Centripetal Force

Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The radius of the earth is 6.37 x 10⁶ m, and the altitude of a geosynchronous orbit is 3.58 x 10⁷ m (≈ 22,000 miles). What are (a) the speed and (b) the magnitude of the acceleration of a satellite in a geosynchronous orbit?

Uniform Circular Motion | Physics with Professor Matt Anderson | M8-01

Circular Orbit of the Moon

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Satellite Motion:Speed & Period

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Overview of Kepler's Laws

Period and Frequency in Uniform Circular Motion

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