A rotating wheel of radius 0.5 m has an angular velocity of 5 rad/s at some instant and 10 rad / s after 5 s. Find the angular acceleration of a point on its rim.
Correct answer: A. 1 rad/s2
- A. 1 rad/s2
- B. 3 rad/s2
- C. 5 rad/s2
- D. 7 rad/s2
- E. 9 rad/s2
Explanation
The angular acceleration of a rotating object can be found using the formula α = (ωf - ωi) / t, where ωf is the final angular velocity, ωi is the initial angular velocity, and t is the time interval. In this case, the initial angular velocity (ωi) is 5 rad/s, the final angular velocity (ωf) is 10 rad/s, and the time interval (t) is 5 seconds. Substituting these values into the formula gives: α = (10 rad/s - 5 rad/s) / 5 s = 1 rad/s2. Therefore, Option A is correct. All other options are incorrect as they do not result from applying this formula to the given values.
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About Angular Velocity
Angular velocity describes how quickly angular displacement changes with time, with ω = Δθ/Δt and units of radians per second. Questions relate angular and linear motion through v = rω, use the direction given by the right hand rule, and distinguish angular velocity from angular acceleration and ordinary frequency.
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