The rate of rotation of a solid disk with a radius of $4 m$ $4 m$ and mass of $5 k g$ $5 kg$ constantly changes from $16 H z$ $16 Hz$ to $5 H z$ $5 Hz$ . If the change in rotational frequency occurs over $7 s$ $7 s$ , what torque was applied to the disk?

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Answer 1 · 2016-12-10T06:24:31

The torque is $= 237 k g m^{2} s^{- 1}$ $=237kgm^2s^(-1)$

The torque is $τ = I α$ $tau=Ialpha$

$τ = I \frac{d ω}{d t}$ $tau=I(domega)/dt$

The moment of inertia of a solid disc $I = \frac{m r^{2}}{2}$ $I=(mr^2)/2$

$I = 3 \cdot \frac{4^{2}}{2} = 3 \cdot 8 = 24 k g m^{2}$ $I=3*4^2/2=3*8=24 kg m^2$

$\frac{d ω}{d t} = \frac{16 - 5}{7} \cdot 2 π = (\frac{22}{7} π) r a d s^{- 1}$ $(domega)/dt=(16-5)/7*2pi=(22/7pi )rads^(-1)$

So, the torque is

$τ = 24 \cdot \frac{22}{7} π = 237 k g m^{2} s^{- 1}$ $tau=24*22/7pi=237kgm^2s^(-1)$

The rate of rotation of a solid disk with a radius of 4m4 m and mass of 5kg5 kg constantly changes from 16Hz16 Hz to 5Hz5 Hz. If the change in rotational frequency occurs over 7s7 s, what torque was applied to the disk?