Question
A gear with a mass moment of inertia of 0.45 kg⋅m^2 has a kinetic energy of rotation of 21 joules.
A gear with a mass moment of inertia of 0.45 kg⋅m^2 has a kinetic energy of rotation of 21 joules. What is its speed of rotation in rpm?
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Koala Tutor
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The kinetic energy of rotation is given by the formula:
KE = 0.5 * I * ω^2
where KE is the kinetic energy, I is the mass moment of inertia, and ω is the angular velocity in rad/s.
We can rearrange this formula to solve for ω:
ω = sqrt((2 * KE) / I)
Substituting the given values:
ω = sqrt((2 * 21 joules) / 0.45 kg⋅m^2) = sqrt(93.33 rad^2/s^2) = 9.66 rad/s
To convert this to rpm (revolutions per minute), we use the conversion factor 60/(2π):
ω = 9.66 rad/s * 60/(2π) = 92.2 rpm
So the speed of rotation is approximately 92.2 rpm.
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