Pure Rotational Motion!

Classical Mechanics Level 3

The moment of inertia of a body about a given axis is $1.2kg~m^{2}$ . Initially the body is at rest. In order to produce a Rotational Kinetic Energy of $1500J$ an angular acceleration of $25rad~s^{-2}$ must be applied about the axis of rotation for a duration of how many seconds ?????

t=20s

t=10s

t=6s

t=8s

t=\pi~seconds

t=4s

t=2s

t=1~min

1 solution

Muhammad Arifur Rahman
May 7, 2015

Its not so complex, as its Pure Rotational Motion ! Here, Kinetic Energy (Rotational) $\text{E}=1500J$ Moment of Inertia $\text{I}=1.2kg.m^2$ You know, $\text{E}=\frac{1}{2} I\omega^2$ $or, \omega=\frac{2\text{E}}{I}$ $=50 rad/s$ And $\omega=\omega_0 +\alpha t$

Here, $\omega_0=0 ,\text{As was at rest}$ $\alpha=25 rad/s^2$ So, $t=\frac{\omega}{\alpha}$ $=\boxed{2 sec}$

If you're a newbie on Rotational Motion, have a look at HyperPhysics Rotational Motion !

Have a nice Rolling Day!!!

I am not a newbie on Rotational Motion @Arifur Rahman !!!! Its just that i couldn't think of any other apt name for the problem !!!!!!

Gagan Raj - 6 years, 1 month ago

Eeee.... I meant You to be the Next Learners who would try to solve this brilliant problem. You're not a newbie, you're genius.

And your Title of this Problem is absolutely appropriate and brilliant. 'Cause your brilliant Title attracted my attention ! And you're requested to Upvote the solution, as you're the Problem Setter !

....Have a good day!

Muhammad Arifur Rahman - 6 years, 1 month ago

Well i dint quite get your idea @Arifur Rahman but now i am clear and yes i am not a genius yet. Good solution though. You've gained my upvote. Enjoy And Learn !!!!!

Gagan Raj - 6 years, 1 month ago

@Gagan Raj – You're so humble, like the Gagan, the Sky!

Muhammad Arifur Rahman - 6 years, 1 month ago

Pure Rotational Motion!

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