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Rotational Motion

Rotational Motion. AP Physics C. Introduction. The motion of a rigid body (an object with a definite shape that does not change) can be analyzed as the translational motion of its center of mass AND the rotational motion about its center of mass.

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Rotational Motion

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  1. Rotational Motion AP Physics C

  2. Introduction • The motion of a rigid body (an object with a definite shape that does not change) can be analyzed as the translational motion of its center of mass AND the rotational motion about its center of mass. • All points on a rotating rigid body move in circles and the center of these circles lie on a line called the axis of rotation

  3. Axis of Rotation Axis of Rotation

  4. Angular Displacement • Angular Displacement • Symbol: θ • Unit: radian, rad • 360° = 2π radians • 1 rad = 57.3°

  5. Angular Velocity • Angular Velocity • Symbol: ω • Unit: rad/s • Direction: use RHR • Every point on a rotating rigid body has the same ω

  6. Angular Acceleration • Angular Acceleration • Symbol: α • Unit: rad/s2 • Direction: See figure • Every point on a rotating rigid body has the same α

  7. Angular Acceleration

  8. Δθ ω α Δx v a Angular & Linear Analogies In rotational motion if you know the analogous quantity in the linear realm all you do is replace the linear quantity with the angular quantity and you have the angular equation

  9. Relating Angular to Linear

  10. Moment of Inertia aka Rotational Inertia • The tendency of a body to resist a rotation Unit: kgm2 See board for derivation

  11. Rotational Kinetic Energy This is not a new form of energy, rather it is the sum of the individual kinetic energies of the individual particles of the rigid body written in a compact and convenient form.

  12. Energy is still conserved

  13. Parallel Axis Theorem The moment of inertia for an axis through the center of mass is lower than for any parallel axis

  14. Moment of Inertia with Calculus

  15. Rotational Dynamics: What causes rotational motion? • An applied force causes motion therefore an applied force is necessary to make a body rotate but where that force is applied will also determine the rotation of the body

  16. Torque • The quantitative measure of the tendency of a force to cause or change the rotational motion of a body. • “Angular force” Direction use RHR Unit: m • N

  17. Magnitude of Torque lever arm vs F┴

  18. Rotational analogy for Newton’s 2nd Law (rigid bodies only)

  19. Work and Power in Rotational Motion

  20. Angular Momentum Unit: kgm2/s

  21. Newton’s 2nd Law’s Rotational Analog in terms of angular momentum

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