Concept explainers
When the gear rotates 20 revolutions, it achieves an angular velocity of ω = 30 rad/s, starting from rest. Determine its constant angular acceleration and the time required.
The gear’s constant angular acceleration and the time required to achieve the angular velocity
Answer to Problem 1FP
The gear’s constant angular acceleration
Is
The time required to achieve the angular velocity
Explanation of Solution
Given:
The angular acceleration
Final angular velocity
The angular displacement of gear
Write the expression of angular displacement for gear.
Write the equation of the angular acceleration.
Here, angular acceleration is
Write the expression for the angular velocity.
Here, angular velocity is
Write the expression for the angular velocity.
Here, angular velocity is
Conclusion:
Substitute
Thus, the gear’s constant angular acceleration
Substitute
Thus, the time required to achieve the angular velocity
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