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Uniform Circular Motion

Uniform Circular Motion. Speed and Velocity. Uniform circular motion is the motion of an object in a circle with a constant or uniform speed. Math Vocabulary. C ircumference :The distance of one complete cycle around the perimeter of a circle. Units are meters (m)

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Uniform Circular Motion

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  1. Uniform Circular Motion

  2. Speed and Velocity • Uniform circular motion is the motion of an object in a circle with a constant or uniform speed.

  3. Math Vocabulary • Circumference:The distance of one complete cycle around the perimeter of a circle. Units are meters (m) • Period: The time it takes for one full rotation or revolution of an object. Units are seconds (s) • Frequency: The number of rotations or revolutions per unit time. Units are inverse seconds (1/s) or Hertz (Hz)

  4. Math Vocabulary

  5. Linear or Tangential Speed • Circumference = 2πr • Average Speed = Circumference/T where T is the period in seconds. Combining the equations results in…. v = 2πr/T v is the linear or tangential speed because at any given time, the velocity is tangent to the circle.

  6. Linear or Tangential Speed

  7. Centripetal Acceleration • An object can move around in a circle with a constant speed yet still be accelerating – why? • Its direction is constantly changing. • The acceleration is directed toward the center of the circle – this is centripetal acceleration. • Centripetal acceleration = (linear speed)2/radius or ac = v2/r Units are m/s2

  8. Direction of ac

  9. Centripetal Force • If a mass is accelerated toward the center of a circle, it must be acted upon by an unbalanced force – centripetal force. • Centripetal force is always directed towards center of the circle • Centripetal force = (mass)(centripetal acceleration) • Fc = mac Units are N

  10. Fc

  11. Torque • A measurement of the tendency of a force to produce a rotation about an axis. • Torque = perpendicular force x lever arm • τ = F x d N-m is the unit

  12. Direction of Rotation • Counterclockwise around the fulcrum is a positive torque • Clockwise around the fulcrum is a negative torque. • When objects are balanced, the sum of all torques acting on the object are zero.

  13. Center of Gravity • The point on any object that acts like the place at which all the weight is concentrated. • Weight of an object can produce torque (cause it to rotate) if the object is not supported at its center of gravity.

  14. Stable vs. Unstable • If the cg is above the area of support, the object will remain upright – otherwise, it will topple.

  15. Toppling • The cg of an object has a tendency to take the lowest position available. • The center of gravity is lowered when toppling occurs.

  16. Rotational Inertia • The greater an object’s rotational inertia, the more difficult it is to change the rotational speed of the object. • Rotational Inertia depends on mass as well as the distribution of the mass. The further the mass is from the axis of rotation, the greater the inertia.

  17. Rotational Inertias of Various Objects are Different:

  18. Rotational Inertia and Rolling • Objects of the same shape but different sizes accelerate equally when rolled down an incline. (Same rotational inertia per kg)

  19. Angular Momentum • The measure of how difficult it is to stop a rotating object • Angular momentum = (mass)(velocity)(radius) • L = mvr • Units are kgm2/s

  20. Conservation of Momentum • When no outside torques are acting, momentum is conserved. • Example: Skater spinning.

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