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Answer :
Final answer:
The wheel, undergoing constant angular acceleration, has rotated through an angle of 270 radians after 10 seconds.
Explanation:
The question asks for the angle a wheel has rotated through given an angular acceleration of 5.0 rad/s² and an initial angular velocity of 2.00 rad/s over a time period of 10 seconds. To solve this, we can use the kinematic equation for rotational motion:
θ = ω₀t + ½ αt²
Where:
- θ is the angle of rotation in radians
- ω₀ is the initial angular velocity in rad/s
- t is the time in seconds
- α is the angular acceleration in rad/s²
Plugging in the values:
θ = (2.00 rad/s)(10 s) + ½(5.0 rad/s¸)(10 s)²
θ = 20.00 rad + ½(5.0 rad/s²)(100 s²)
θ = 20.00 rad + 250.00 rad
θ = 270.00 rad
Therefore, the wheel has rotated through an angle of 270 radians in 10 seconds under the given conditions.
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