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Circular Motion

Circular Motion. = the movement of an object at constant speed around a circle with fixed radius Axis – straight line around which rotation takes place Rotation – object turns around an internal axis Ex. Ice skater Revolution – object turns around an external axis Ex. Earth around the sun.

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Circular Motion

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  1. Circular Motion • = the movement of an object at constant speed around a circle with fixed radius • Axis – straight line around which rotation takes place • Rotation – object turns around an internal axis • Ex. Ice skater • Revolution – object turns around an external axis • Ex. Earth around the sun

  2. Rotational Speed • Linear speed – distance/time • Tangential speed – speed along a circular path • Rotational speed – number of rotations per unit of time • Example: Carousel horses travel at same rotational speed but different tangential speed

  3. Linking tangential and rotational speed • Tangential speed is radial distance times the rotational speed • V = r ω

  4. Centripetal Force • Force that causes an object to follow a circular path • Ex. Force holding occupants safely in a rotating carnival ride • Fnet = mv2 r

  5. Centripetal Acceleration • Always points toward the center of the circular motion. • Period (T) = time needed for an object to make one complete revolution • Distance traveled = circumference • Circumference = 2πr = πd

  6. Other formulas • Centripetal Acceleration equals the velocity squared divided by the radius • Ac = v2/r • The number of revolutions equals the distance traveled divided by the circumference • Revolutions = distance/circumference

  7. Sample problems • If a wheel has a diameter of 0.51 m and the wheel travels for 15 m, how many revolutions will it make? • What is the tension in a 3.2 m length of string that whirls a 1.5 kg mass at 2.1 m/s in a horizontal circle?

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