Questions: B6-CRT02: ANGULAR VELOCITY-TIME GRAPH-ANGULAR ACCELERATION-TIME GRAPH Sketch an angular acceleration versus time graph given the angular velocity versus time graph shown for the same time interval. Explain your reasoning.

Solution Steps

The given angular velocity-time graph has three distinct segments:

1. A linear increase in angular velocity.
2. A constant angular velocity.
3. A linear decrease in angular velocity.

1. Linear increase in angular velocity: Angular acceleration (α) is the slope of the angular velocity (ω) vs. time (t) graph. Since ω is increasing linearly, α is constant and positive.
2. Constant angular velocity: When ω is constant, the slope is zero, so α is zero.
3. Linear decrease in angular velocity: Angular acceleration (α) is the slope of the ω vs. t graph. Since ω is decreasing linearly, α is constant and negative.

1. For the first segment (linear increase in ω), draw a horizontal line above the time axis indicating a positive constant α.
2. For the second segment (constant ω), draw a horizontal line on the time axis indicating α = 0.
3. For the third segment (linear decrease in ω), draw a horizontal line below the time axis indicating a negative constant α.

Final Answer