A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at a rate of 2 rad/s², what will be its angular velocity after 5 seconds?

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20 rad/s
10 rad/s
30 rad/s
0 rad/s

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Q: A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at a rate of 2 rad/s², what will be its angular velocity after 5 seconds?

Solution: Final angular velocity = initial angular velocity + (angular acceleration × time) = 10 + (2 × 5) = 20 rad/s.

Steps: 8

Step 1: Identify the initial angular velocity. In this case, it is 10 rad/s.
Step 2: Identify the angular acceleration. Here, it is 2 rad/s².
Step 3: Identify the time duration for which the wheel accelerates. This is 5 seconds.
Step 4: Use the formula for final angular velocity: Final angular velocity = Initial angular velocity + (Angular acceleration × Time).
Step 5: Substitute the values into the formula: Final angular velocity = 10 rad/s + (2 rad/s² × 5 s).
Step 6: Calculate the product of angular acceleration and time: 2 rad/s² × 5 s = 10 rad/s.
Step 7: Add this result to the initial angular velocity: 10 rad/s + 10 rad/s = 20 rad/s.
Step 8: Conclude that the final angular velocity after 5 seconds is 20 rad/s.

A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at a rate of 2 rad/s², what will be its angular velocity after 5 seconds?

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