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Understanding Circular and Rotational Motion in Physics

Learn about circular motion, Newton's 1st Law, rotational terms, linear speed, centripetal acceleration, and torque in physics with examples and calculations. Enhance your knowledge of motion and forces in this comprehensive guide.

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Understanding Circular and Rotational Motion in Physics

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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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