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Unit 8 Rotational Motion & Universal Gravitation

Unit 8 Rotational Motion & Universal Gravitation. Start a New page in your journal & label “Unit 8”…. Motion. What does Newton’s 1 st law state? Hint: Think Inertia . Motion. What does Newton’s 1 st law state?

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Unit 8 Rotational Motion & Universal Gravitation

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  1. Unit 8Rotational Motion &Universal Gravitation Start a New page in your journal & label “Unit 8”…

  2. Motion • What does Newton’s 1st law state? • Hint: Think Inertia

  3. Motion • What does Newton’s 1st law state? • An object in motion will remain in motion unless another force acts on the object

  4. So, Rotational Motion… • Newton’s law also applies to rotational motion, we call this rotational inertia • So, an object in rotation will continue to rotate unless another force acts on the object.

  5. Rotation vs. Revolution • “Rotation” is different than “Revolution” • Rotation is moving around an axis (internal) • Example: Earth spinning on its axis, takes 24 hours • Revolution is moving around an object (external axis) • Example: Earth traveling around the sun, takes ~365 days.

  6. Rotational Motion: Center of Gravity • We base motion around an object’s center of gravity which is also known as the center of mass • The average position of all of an objects weight. • It is the center of all of the objects mass.

  7. Rotational MotionTypes of Speed v

  8. ? • What do the arrows represent? • Which insect has a faster tangential speed?

  9. Practice Problems • An elementary student passes through a revolving door, all the way around, in 10 seconds. If he is 0.80m from the center of the door, what is the door's tangential speed?

  10. Practice Problems • An elementary student passes through a revolving door, all the way around, in 10 seconds. If he is 0.80m from the center of the door, what is the door's tangential speed?

  11. Practice Problems • An athlete spins in a circle before releasing a discus in 3 seconds. What is the tangential speed of the spinning athlete? Assume the discus is .75m from the athlete's axis for rotation.

  12. Practice Problems • An athlete spins in a circle before releasing a discus in 3 seconds. What is the tangential speed of the spinning athlete? Assume the discus is .75m from the athlete's axis for rotation.

  13. Practice Problems • An athlete spins in a circle before releasing a discus in 3 seconds. What is the tangential speed of the spinning athlete? Assume the discus is .75m from the athlete's axis for rotation.

  14. Rotational MotionTypes of Speed

  15. ? • What do the circles represent? • Which insect has a faster rotational speed?

  16. Linear vs. Rotational VelocityFormulas

  17. Review • Rotation • Revolution • Linear/Tangential Speed V = 2πr/T • Rotational/Angular Speed ω = 2πT

  18. Uniform Circular Motion • Uniform circular motion is when an object travels in a circle with a constant speed. • The velocity vector is always tangent to the circle and has a constant magnitude.

  19. Centripetal Acceleration • Remember that acceleration is a change in velocity OR direction. • Since the direction of the velocity changes continuously as the object moves around the circle, it is constantly being accelerated. • This acceleration is known as centripetal acceleration.

  20. Centripetal Acceleration • Centripetal acceleration is given by the formula ac= v2 / r • Where ac = centripetal acceleration • v = velocity of object accelerating • r = radius of whatever is being orbited The force causing the acceleration is in the same direction and is known as centripetal force.

  21. Centripetal Force • An object moving in a circular motion is constantly accelerating. • In order to accelerate it must have a net force acting upon it. • Remember that F= ma • Therefore Fc=mac= mv2/r

  22. Centripetal Force • Many things can cause centripetal force • A string attached to a tetherball • The gravity of the Earth and the moon causing the moon to orbit the earth. • Friction on the tires of a car as it drives around a circular track

  23. Centripetal Force • If an object were to lose centripetal force it would leave it’s circular path and travel in a straight line.

  24. At point P, the car hitsan area of ice and losesall frictional force on its tires. Which path does the car follow on the ice?

  25. Period • The period of revolution (T) is the time it takes for the object to move once around the circle. Period is measured in seconds. • You use this basic formula to find how long it takes for an object to move once around the circle. T= Time # of Rotations

  26. Frequency • The number of times that an object moves around a circle in a given period of time. Frequency is measured in Hertz. • Frequency and Period are inverses of each other. • As one increases, the other decreases. • T = 1/f • f = 1/T f = # of Rotations_ Time

  27. Rotational Velocity • Rotational Velocity is found just like linear velocity • v= 2r/T 2r is the circumference of the circle (distance around). T– Period (The time it takes to make one trip around the circle. ) Very similar to v = d/t

  28. Centrifugal Force • Centrifugal Force – The artificial force that pushes away from the center of rotation felt by an object moving in a circle. • Example – Going around a sharp corner in a car.

  29. Bridge 1 • bridge 2 • bridge 3 • bridge 4

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