This is problem from a text book whose solution I don't understand.(adsbygoogle = window.adsbygoogle || []).push({});

A small rock of mass 0.5kg is attached to a 1.5m string, then it is whirled for 5 seconds until it achieves a near horizontal orbit at 120 rpm. What is the torque required?

I used the equation : τ=Iα (moment of inertia x angular acceleration) giving an answer of 2.8 Nm or Joules. This is the book's answer.

My question is, why I don't get the same answer with the formula for rotational kinetic energy

E_k=1/2 Iω^2 which gives 177 Nm.

Both formulas have the same units of Nm or energy. Why the energy used to impart the motion is not the same as the kinetic energy stored in the moving mass?

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# Torque and rotational kinetic energy

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