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University Physics: Mechanics

University Physics: Mechanics. Ch 4 . TWO- AND THREE-DIMENSIONAL MOTION. Lecture 6. Dr.-Ing. Erwin Sitompul. http://zitompul.wordpress.com. Uniform Circular Motion. A particle is in uniform circular motion if it travels around a circle or a circular arc at constant ( uniform ) speed.

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University Physics: Mechanics

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  1. University Physics: Mechanics Ch4. TWO- AND THREE-DIMENSIONAL MOTION Lecture 6 Dr.-Ing. Erwin Sitompul http://zitompul.wordpress.com

  2. Uniform Circular Motion • A particle is in uniform circular motion if it travels around a circle or a circular arc at constant (uniform) speed. • Although the speed does not vary, the particle is accelerating because the velocity changes in direction. • The velocity is always directed tangent to the circle in the direction of motion. • The acceleration is always directed radially inward. • Because of this, the acceleration associated with uniform circular motion is called a centripetal (“center seeking”) acceleration.

  3. Uniform Circular Motion → • The magnitude of this centripetal acceleration a is: (centripetal acceleration) where r is the radius of the circle and v is the speed of the particle. • In addition, during this acceleration at constant speed, the particle travels the circumference of the circle (a distance of 2πr) in time of: (period) with T is called the period of revolution, or simply the period, of the motion.

  4. Checkpoint An object moves at constant speed along a circular path in a horizontal xy plane, with the center at the origin. When the object is at x = –2 m, its velocity is –(4 m/s) j. Give the object’s (a) velocity and (b) acceleration at y = 2 m. ^ ^ → v2 = –4 m/s i 2 m ^ → v1 = –4 m/s j ^ → a = –8 m/s2 j → → → v2 a v1

  5. Example: Fighter Pilot Fighter pilots have long worried about taking a turn too tightly. As a pilot’s body undergoes centripetal acceleration, with the head toward the center of curvature, the blood pressure in the brain decreases, leading to unconsciousness. What is the magnitude of the acceleration, in g units, of a pilot whose aircraft enters a horizontal circular turn with a velocity of vi = 400i + 500j m/s and 24 s later leaves the turn with a velocity of vf = –400i – 500j m/s? ^ ^ ^ ^

  6. Example: Aston Martin An Aston Martin V8 Vantage has a “lateral acceleration” of 0.96g. This represents the maximum centripetal acceleration that the car can attain without skidding out of the circular path. If the car is traveling at a constant speed of 144 km/h, what is the minimum radius of curve it can negotiate? (Assume that the curve is unbanked.) • The required turning radius r is proportional to the square of the speed v • Reducing v by small amount can make r substantially smaller

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