The rate of rotation of a solid disk with a radius of $8 m$ $8 m$ and mass of $5 k g$ $5 kg$ constantly changes from $16 H z$ $16 Hz$ to $22 H z$ $22 Hz$ . 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 · 2016-12-15T06:37:25

The torque is $= 861.7 k g m^{2} s^{- 1}$ $=861.7 kgm^2s^(-1)$

The torque is $τ = I α$ $tau=Ialpha$

$α = \frac{d ω}{d t}$ $alpha=(domega)/dt$

$α = \frac{6}{7} \cdot 2 π r a d s^{- 1} = \frac{12}{7} π r a d s^{- 1}$ $alpha=6/7*2pi rads^(-1)=12/7pi rads^(-1)$

The moment of inertia of a solid disc $I = \frac{1}{2} m r^{2}$ $I=1/2mr^2$

$= \frac{1}{2} \cdot 5 \cdot 8^{2} = 160 k g m^{2}$ $=1/2*5*8^2=160kgm^2$

So,

$τ = 160 \cdot \frac{12}{7} π k g m^{2} s^{- 1} = 861.7 k g m^{2} s^{- 1}$ $tau=160*12/7pi kgm^2s^(-1)=861.7 kgm^2s^(-1)$

The rate of rotation of a solid disk with a radius of 8 m8m8 m and mass of 5 kg5kg5 kg constantly changes from 16 Hz16Hz16 Hz to 22 Hz22Hz22 Hz. If the change in rotational frequency occurs over 7 s7s7 s, what torque was applied to the disk?