What torque would have to be applied to a rod with a length of $1 m$ $1 m$ and a mass of $1 k g$ $1 kg$ to change its horizontal spin by a frequency of $3 H z$ $3 Hz$ over $3 s$ $3 s$ ?

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What torque would have to be applied to a rod with a length of $1 m$ $1 m$ and a mass of $1 k g$ $1 kg$ to change its horizontal spin by a frequency of $3 H z$ $3 Hz$ over $3 s$ $3 s$ ?

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Answer 1 · 2017-02-09T11:12:49

$τ_{net} = \frac{1}{12} \frac{kg m}{s^{2}} \approx 0.833 \frac{kg m}{s^{2}}$ $tau_"net"=1/12 ("kg m")/s^2~~0.833("kg m")/s^2$

Explanation:

Assuming the rod in question rotates about the center (not the end), we know that

Step 1. Gather the information that you know and need

Mass of rod: $mass = m = 1 kg$ $"mass"=m=1" kg"$
Length of rod: $length = L = 1 m$ $"length"=L=1" m"$
Change in angular speed: $d ω = 3 Hz$ $domega=3" Hz"$
Change in time: $d t = 3 s$ $dt=3" s"$
Torque required: ??

Step 2. Determine the formula using the above givens

Torque: $τ_{net} = I α$ $tau_"net"=Ialpha$

$I$ $I$ is the moment of inertia of our rod
Assuming center spin, $I_{rod} = 1 / 12 \cdot m \cdot L$ $I_"rod"=1"/"12*m*L$
$α$ $alpha$ is the instantaneous angular acceleration
$α = d ω / d t$ $alpha=domega"/"dt$ with units $rad/ s^{2}$ $"rad/"s^2$ or $s^{- 2}$ $s^-2$

Torque: $τ_{net} = \frac{1}{12} m L \frac{d ω}{d t}$ $tau_"net"=1/12mL (domega)/dt$

Step 3. Plug your knows into the formula for torque

$τ_{net} = \frac{1}{12} (1 kg) (1 m) \frac{3 Hz}{3 s} = \frac{1}{12} \frac{kg m}{s^{2}}$ $tau_"net"=1/12(1" kg")(1" m")(3" Hz")/(3" s")=1/12("kg m")/s^2$

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What torque would have to be applied to a rod with a length of $1 m$ $1 m$ and a mass of $1 k g$ $1 kg$ to change its horizontal spin by a frequency of $3 H z$ $3 Hz$ over $3 s$ $3 s$ ?

1 Answer

Explanation:

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What torque would have to be applied to a rod with a length of 1m1 m and a mass of 1kg1 kg to change its horizontal spin by a frequency of 3Hz3 Hz over 3s3 s?

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What torque would have to be applied to a rod with a length of $1 m$ $1 m$ and a mass of $1 k g$ $1 kg$ to change its horizontal spin by a frequency of $3 H z$ $3 Hz$ over $3 s$ $3 s$ ?