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Circular Motion

Circular Motion. Newton’s 1 st Law (Inertia) Objects will continue to move with a constant velocity unless acted upon by a net force. Circular Motion. Curved or circular motion is caused by a net force acting perpendicular to the object’s motion

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Circular Motion

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  1. Circular Motion

  2. Newton’s 1st Law (Inertia) Objects will continue to move with a constant velocity unless acted upon by a net force.

  3. Circular Motion Curved or circular motion is caused by a net force acting perpendicular to the object’s motion Force ends up pointing to the center of the circle (centripetal)

  4. Without a centripetal force, an object in motion continues along a straight-line path. With a centripetal force, an object in motion will be accelerated and change its direction.

  5. Examples of Circular Motion • Planets around the sun • FC = gravity from sun • Car driving in circles • FC = friction from road • Carnival ride (you know, the one that spins really fast and the floor drops out and you don’t fall because you’re stuck to the wall) • FC = wall pushing you in

  6. Axis Rotational Motion - Terms • Rotating - occurs when an object turns about an internal axis • Axis - straight line around which rotational motion takes place • Revolving - occurs when an object turns about an external axis

  7. Rotational Motion - Terms • Frequency (f)- the number of revolutions or rotations that occurs in a unit of time • How often • UNITS: Hertz (Hz) (revolutions/second) • Period (T)- the time it takes to complete one revolution or rotation • UNITS: seconds (s) Period = 1/ f Frequency = 1/ T

  8. Linear Speed • Distance moved in a period of time (d/t) • A.K.A. Tangential speed because the velocity is tangent to the circle. • Distance around a circle=2 r • Time to go around a circle=Period(T) • Linear/Tangential speed: v=2 r/T

  9. Linear Speed • Constant speed but changing velocity • Constantly changing directions • Varies with the distance from the axis • Smaller circumference = less distance to travel • Track runners

  10. Rotational Speed • Number of Rotations per unit of time • A.K.A. Angular speed • UNITS: Revolutions per minute (RPM) or revolutions per second (RPS) • All points on a rigid rotating object have the same rotational speed

  11. Circular Motion - Applying Newton’s Laws • Δdirection=Δvelocity • Δvelocity = acceleration • Acceleration is caused by a net force to the center of the circular motion (centripetal) • Net force = mass x ac ac=v2/r Fc =mv2/r

  12. FC

  13. Radius = 36.8 m The distance from the green start line to the red finish line around the curve is 115 m. A runner ran the distance in 15.2 seconds. What is the centripetal acceleration of the runner?

  14. A 2.0 kg body is tied to the end of a cord and whirled in a horizontal circle of radius 2.0 m. If the body makes three complete revolutions every second, determine its linear speed and its centripetal acceleration.

  15. A ball is whirled at the end of a string in a horizontal circle 60 cm in radius at the rate of 1 revolution every 2 s. Find the ball's centripetal acceleration.

  16. A 1000-kg car rounds a turn of radius 30 m at a velocity of 9 m/s. How much centripetal force is required?

  17. Torque Causes an object to rotate Think “leverage” Depends upon perpendicular force applied and length of lever arm Torque = force x length Similar to work: less force=more distance

  18. Examples of torque

  19. Calculate the torque produced by a 50 N perpendicular force at the end of a 0.2 m long wrench.

  20. Balanced Torque • Why does the kid have to sit further back? • Because he is lighter (less FW) • Torque kid = Torque creeper dude

  21. The person on the left has a mass of 75 kg and is 1.4 meters from the center (fulcrum). The person on the right is standing 2 meters from the fulcrum. (A) Should they both sit down before they get hurt? (B) What is the weight of the person on the right?

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