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A wheel initially at rest, is rotated wi...

A wheel initially at rest, is rotated with a uniform angular acceleration. The wheel rotates through an angle `theta_(1)` in the first one second and through an additional angle `theta_(2)` in the next one second. The ratio `theta_(1)//theta_(2)` is:

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Angular displacement in first one second `theta_1=1/2alpha(1)^2=alpha/2`(i) [From`theta=omega_1t+1/2alphat^2`] Now again we will consider motion from the rest and angular displacement in total two seconds `theta_1+theta_1=1/2alpha(2)^2`(ii) Solving (i) and (ii) we get, `theta_1=alpha/2` and`theta_2=(3alpha)/2. because theta_2/theta_1=3`.
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