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Question

A wheel rotates with a constant angular acceleration of 2rad/s2. The total acceleration of the wheel becomes 13.6rad/s2after 1s of the beginning of motion. Determine the radius of the wheel.


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Solution

Step 1: Given data:
Constant angular acceleration α=2rad/s2
Total acceleration of the wheel a=13.6rad/s2
Time t=1s

Step 2: To find acceleration:

The acceleration of the wheel is given by,
a=ar2+at2,
The tangential acceleration of the wheel is
at=rα=2r,
The radial acceleration ar=ω2r ,
where, r is the radius, ω is the angular velocity αis the angular acceleration. It is given by,
ω=αt
Therefore,
ar=(αt)2r
ar=(2×1)2r
ar=4r
Step 3: To find the radius:

Therefore,
13.6=(4r)2+(2r)2
13.6=20r2
13.6=4.47r
r=13.64.47
r=3.04m
The radius of the wheel. is 3.04m


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