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Exploration 10.2: Constant Angular Acceleration Equation

θ = + *t + 0.5**t2 (θ is in radians)

check, then click set values and play to see "ghost" images set at equal time intervals to mark the path of the ball.

Please wait for the animation to completely load.

By now you have seen the equation:  θ = θ0+ ω0*t + 0.5*α*t2. Perhaps you have even derived it for yourself. But what does it really mean for the motion of objects? This Exploration allows you to explore all three terms in the equation: the initial angular position by changing θ0 from 0 radians to 6.28 radians, the angular velocity term by changing ω0 from -15 rad/s to 15 rad/s, and the angular acceleration by changing α from -5 rad/s2 to 5 rad/s2. Restart.

Answer the following questions (position is given in meters and time is given in seconds).

  1. How does changing the initial angular position affect the motion of the object?
  2. How does changing the initial angular velocity affect the motion of the object?
  3. How does changing the angular acceleration affect the motion of the object?
  4. Can you get the object to change direction?

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