A circular disc is rotating about its own axis with a constant angular acceleration.If its angulat velocity increases fron 210 rpm to 420rpm during 21 rotation then the angular acceleration of the disc is
Answers
The angular acceleration of the disc is 5.5 rad/s²
Explanation:
=> The initial angular velocity, ωi :
ωi = 210 rotation per minute
= 210/60 rotation per second
= 7/2 rotation per second
To convert 7/2 rps to angular velocity, we need to make it θ.
We know, θ = 2*π*no of rps
∴ ωi = θ = 2 x 22/7 x 7/2 = 22
ωi = 22
=> The final angular velocity, ωf:
ωf = 420 rotation per minute
= 420/60 rotation per second
= 7 rotation per second
Similarly, this also has to be converted to θ.
As θ = 2*π*no of rps
∴ ωf = θ = 2 x 22/7 x 7
ωf = 44
=> According to the question, no of rotations = 21
if we converted it to θ, then
θ = 2*π*no of rotation
= 2 * 22/7 * 21
= 132
=> Angular acceleration of the disc, α:
α = ωf² - ωi² / 2θ
= 44² - 22² / 2*132
= 1936 - 484 / 264
= 1452 / 264
= 5.5 rad/s²
Thus, the angular acceleration of the disc is 5.5 rad/s².
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