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Question
The moment of inertia of a body about a given axis is 1.2 kgm2. initially, the body is at rest. For what duration on the angular acceleration of 25 radian/sec2 must be applied about that axis in order to produce rotational kinetic energy of 1500 joule?
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Solution
Given:
I = 1.2 kgm2, α = 25 radian/sec2, ω0 = 0 rad/s, (K.E.)rot = 1500 J
To find: Time (t)
Formulae:
i. α = `(ω - ω_0)/t`
ii. K.E. = `1/2"Iω"^2`
Calculation:
From formula (i),
25 = `(ω - 0)/t`
∴ ω = 25t
From formula (ii),
1500 = `1/2 xx 1.2 xx (25t)^2`
∴ t = `sqrt((2 xx 1500)/(1.2 xx 25^2)) = sqrt4`
∴ t = 2 sec.
An angular acceleration must be applied for 2 sec.
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