A wheel is rotating about its axis with angular acceleration at time 't' given by α = 6t²+ 2, where α is in rad/s² and t is in second. When t = 0, the position is taken as zero and then its angular velocity is 5 rad/s. What would be angular velocity at t = 10 s?

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BHEL Engineer Trainee Mechanical 24 Aug 2023 Official Paper

Answer 1

Concept:

The angular acceleration is given by, \( \alpha = 6t^2 + 2 \)

The relation between angular velocity and angular acceleration is:

\( \frac{d\omega}{dt} = \alpha \)

Integrating both sides:

\( \omega = \int (6t^2 + 2) dt \)

\( \omega = 2t^3 + 2t + C \)

At t = 0, the initial angular velocity is \( \omega_0 = 5 \) rad/s.

Substituting in the equation:

\( 5 = 2(0)^3 + 2(0) + C \Rightarrow C = 5 \)

Thus, the equation for angular velocity is:

\( \omega = 2t^3 + 2t + 5 \)

At t = 10 sec,

\( \omega = 2(10)^3 + 2(10) + 5 \)

\( \omega = 2(1000) + 20 + 5 \)

\( \omega = 2025~rad/s\)