PHYS 2211 Study Guide - Midterm Guide: Acceleration, Centripetal Force, Centrifugal Force

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burgundyhound215

30 Mar 2019

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Key ideas: circular motion & gravitation: the period of an object in circular motion is the time needed for the object to make one complete circle or orbit. Period, t, is equal to the orbit circumference divided by the tangential velocity. T = 2 r/v: as an object travels in a curved path, the direction of its velocity changes. Centripetal acceleration is the name given to a change in velocity due to curved motion. Centripetal force is the name for the "net force toward the center of the circle" that causes circular motion to occur. Centrifugal force is the name for the apparent force that "pushes" objects away from the center of a circle from the viewpoint of the object that is undergoing circular motion. Your sense of weight arises from the normal force on you: g"s or force factor = fn / fg tells how many times heavier than usual a person feels.

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This experiment involves centripetal force, the force that keeps objects moving in a circular path. This force is perpendicular to the motion and directed towards the center of the circular orbit. By Newton's Second Law when a centripetal force acts on a mass (in a horizontal plane), the force continually changes the direction of the velocity without changing its magnitude, speed. This change in the direction of the velocity accounts for the centripetal acceleration of the mass, whose direction is towards the center. The relationship between the centripetal force, the mass of the orbiting object, and its speed and distance from the center is described by:

EXTENSION QUESTION: When twirling the mass, students found that despite their best efforts, they could not swing the ball so that the cord remained exactly horizontal.

(a) On the diagram of the rotating mass below, draw a force diagram of the forces acting on the mass and identify each force. Do not include any force components in this diagram.

(b) Explain why it is not possible for the ball to swing so that the cord remains exactly horizontal. Write your answer using complete sentence

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14.82 CP An interesting, though highly impractical example of oscillation is the motion of an object dropped down a hole that extends from one side of the earth, through its center, to the other side. With the assumption (not realistic) that the earth is a sphere of uniform density, prove that the motion is simple harmonic and find the period. [Note: The gravitational force on the object as a function of the object's distance r from the center of the earth was derived in Example 13.10 (Section 13.6). The motion is simple harmonic if the acceleration at and the displacement from equilib- rium x are related by Eq. (14.8), and the period is then T = 27/.]

A particle P moves with constant angular speed ω around a circle whose center is at the origin and whose radius is R.The particle is said to be in a uniform circular motion. Assume that the motion is counterclockwise and that the particle is at the point (R, 0) when t = 0.The position vector at time t ≥ 0 is r(t) = R cos ωt i + R sin ωt j.

(a) Find the velocity vector v and show that v · r = 0. Conclude that v is tangential to the circle and points in the direction of the motion.

(b) Show that the speed of the particle is constant ωR. The period T of the particle is the time required for one complete revolution. Conclude T = 2π/ω.

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PHYS 2211 Study Guide - Midterm Guide: Acceleration, Centripetal Force, Centrifugal Force

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