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TYPES OF MOTION
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TRANSLATION (or linear) – motion along a path; measureable quantities include both position and velocity
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ROTATIONAL – spinning at a constant rate about a vertical axis
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CIRCULAR – set of motion along an orbit
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about an external point
object moves in circular path about an external point (“revolves”)
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According to Newton’s First Law of Motion,
objects move in a straight line unless a force makes them turn. An external force is necessary to make an object follow a circular path. This force is called a CENTRIPETAL (“center seeking”) FORCE. Since every unbalanced force causes an object to accelerate in the direction of that force (Newton’s Second Law), a centripetal force causes a CENTRIPETAL ACCELERATION. This acceleration results from a change in direction, and does not imply a change in speed, although speed may also change.
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v = 2pr/T v r m gravity - planets orbiting the sun
Centripetal force and acceleration may be caused by: gravity - planets orbiting the sun friction - car rounding a curve a rope or cord - swinging a mass on a string In all cases, a mass m moves in a circular path of radius r with a linear speed v. The time to make one complete revolution is known as the period, T. The speed v is the circumference divided by the period. v r m v = 2pr/T
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ac = v2/r Fc = mac = mv2/r and centripetal force (Fc) is:
The formula for centripetal acceleration (ac) is: ac = v2/r and centripetal force (Fc) is: Fc = mac = mv2/r m = mass in kg v = linear velocity in m/s Fc = centripetal force in N r = radius of curvature in m ac = centripetal acceleration in m/s2
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(“rotates” or “spins”)
object moves in circular path about an internal point or axis (“rotates” or “spins”)
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degrees, radians, or rotations. deg/s, rad/s, rpm, etc...
The amount that an object rotates is its angular displacement. angular displacement, q, is given in degrees, radians, or rotations. 1 rotation = 360 deg = 2p radians The change in an object’s angular displacement over time is its angular velocity. angular velocity, w, is given in deg/s, rad/s, rpm, etc...
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The change in an object’s angular velocity over time is its
angular acceleration. Angular acceleration, a, is given in deg/s2, rad/s2, rpm/s, etc... Formulas for rotational motion follow an exact parallel with linear motion formulas. The only difference is a change in variables and a slight change in their meanings.
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TRANSLATIONAL (LINEAR) AND
ROTATIONAL FORMULA TRANSLATIONAL ROTATIONAL wf = wi + at vf = vi + at q = wavt d = vavt ωav= (wf + wi)/2 vav = (vf + vi)/2 d = vit + ½ at2 q = wit + ½ at2 vf2 = vi2 + 2ad wf2 = wi2 + 2aq
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