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    5.2. Circular Motion PDF

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    jmsonl
    This document discusses key concepts in circular motion including: - Radians are used to measure angles, with 2π radians in a full circle. Angular velocity is the rate of change of the angle. - Period is the time for one full circle, and frequency is the number of circles per second. They are related by f=1/T. - Centripetal force is the net force acting towards the center of the circle, and is provided by gravitational force, tension, etc. It is given by F=mv2/r.

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    5.2. Circular Motion PDF

    Uploaded by

    jmsonl
    103 views3 pages
    This document discusses key concepts in circular motion including: - Radians are used to measure angles, with 2π radians in a full circle. Angular velocity is the rate of change of the angle. - Period is the time for one full circle, and frequency is the number of circles per second. They are related by f=1/T. - Centripetal force is the net force acting towards the center of the circle, and is provided by gravitational force, tension, etc. It is given by F=mv2/r.

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    5.2. Circular Motion.pdf

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    This document discusses key concepts in circular motion including: - Radians are used to measure angles, with 2π radians in a full circle. Angular velocity is the rate of change of the angle. - Period is the time for one full circle, and frequency is the number of circles per second. They are related by f=1/T. - Centripetal force is the net force acting towards the center of the circle, and is provided by gravitational force, tension, etc. It is given by F=mv2/r.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    103 views3 pages

    5.2. Circular Motion PDF

    Uploaded by

    jmsonl
    This document discusses key concepts in circular motion including: - Radians are used to measure angles, with 2π radians in a full circle. Angular velocity is the rate of change of the angle. - Period is the time for one full circle, and frequency is the number of circles per second. They are related by f=1/T. - Centripetal force is the net force acting towards the center of the circle, and is provided by gravitational force, tension, etc. It is given by F=mv2/r.

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    OCR A Physics A-level

    Topic 5.3: Circular motion


    Notes

    www.pmt.education
    Kinematics of circular motion
    The radian
    Radians can be used instead of degrees to measure angles. A radian is the angle subtended by a
    circular arc with a length equal to the radius of the circle. There are 2π radians in a full circle. To
    convert an angle from degrees to radians, divide it by 360 and then multiply by 2π.
    Period and frequency
    The period, T, is the time, in seconds, taken for an object to travel a full circle. The frequency, f,
    measured in Hertz (Hz) is the number of full circles completed in one second. The two are
    related by the formula f = 1/T.
    Angular velocity
    The angular velocity, ω, of an object moving in a circle is the rate of change of angle. It is
    𝜃𝜃
    given by the formula 𝜔𝜔 = 𝑡𝑡 , where θ is the angle the object has travelled through in the time t. It
    is measured in rads-1, so the angle must be measured in radians and the time in seconds. In a time
    of one period, T, the object will complete a full circle, with an angle equal to 2π radians. The
    formula for angular velocity can therefore be written as
    2𝜋𝜋
    𝜔𝜔 = = 2𝜋𝜋𝜋𝜋
    𝑇𝑇

    Centripetal force
    Centripetal force
    When an object travels in a circle, its direction is constantly changing. As velocity is given with
    respect to direction, this means the velocity of the object is also constantly changing, even
    though the speed maybe constant. In order for the velocity to change, the object must be
    accelerating, and this acceleration is provided by the centripetal force. Centripetal force is the
    net force which acts perpendicular to the direction of the velocity, towards the centre of the
    circle.
    The speed v of a object moving in a circle of radius r is given by the formula
    2𝜋𝜋𝜋𝜋
    𝑣𝑣 = = 𝜔𝜔𝜔𝜔
    𝑡𝑡
    The acceleration of the object is equal to the rate of change of velocity. The centripetal
    acceleration for an object moving in a circle is given by the formula
    𝑣𝑣 2
    𝑎𝑎 = = 𝜔𝜔2 𝑟𝑟
    𝑟𝑟

    www.pmt.education
    Using the formula F=ma, the centripetal force can be determined by substituting in the
    expression for centripetal acceleration, to give
    𝑚𝑚𝑣𝑣 2
    𝐹𝐹 = = 𝑚𝑚𝜔𝜔2 𝑟𝑟
    𝑟𝑟
    The centripetal force can come from many places, e.g. gravitational fields, friction, tension in a
    rope. It is important to remember that centripetal force is the net force acting towards the centre
    of the circle, so when an object experiences multiple forces (such as normal contact force acting
    in and gravitational force acting out) the resultant force must be used.
    Techniques to investigate circular motion
    Circular motion can be investigated experimentally by tying a
    bung, with mass m, to a piece of string, and threading it through
    a glass tube. The other end of the string has a weight, with mass
    M, suspended from it. This provides the centripetal force, F =
    Mg, as the tension throughout the string is constant. The string is
    whirled in a circle, and the time taken for a complete rotation is
    recorded. The mass of the weight is altered and the experiment
    repeated.
    𝑚𝑚𝑣𝑣 2
    As the centripetal force is given by the formula , and provided by the weight on the end of
    𝑟𝑟
    the string, Mg, we can equate the two to get
    𝑚𝑚𝑣𝑣 2
    𝑀𝑀𝑀𝑀 =
    𝑟𝑟
    By measuring the radius of the circle and using the time for one complete oscillation, the
    velocity can be determined. When v2 is plotted against M, a straight line graph which passes
    through the origin should be produced.

    www.pmt.education

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