An object starts from rest accelerates at a constant rate in a circular path. After a certain time t the object reaches the angular velocity ω. How many revolutions sis it make during time t?
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Explanation:
You may recall the kinematic equation that relates final velocity, initial velocity, acceleration, and distance, respectively:
v2f=v2i+2ad
Well, for rotational motion (such as in this problem), there is a similar equation, except it relates final angular velocity, intial angular velocity, angular acceleration, and angular distance, respectively:
ω2f=ω2i+2αθ
The wheel starts at rest, so the initial angular velocity, ωi, is zero. The total number of revolutions of the wheel is given to be 5 revolutions. Each revolution is equivalent to an angular distance of 2π radians. So, we can convert the total revolutions to an angular distance to get:
θ=5rev⋅2π1rev=10π
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