An object with a mass of $3 k g$ $3 kg$ is traveling in a circular path of a radius of $2 m$ $2 m$ . If the object's angular velocity changes from $1 H z$ $1 Hz$ to $3 H z$ $3 Hz$ in $5 s$ $5 s$ , what torque was applied to the object?

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An object with a mass of $3 k g$ $3 kg$ is traveling in a circular path of a radius of $2 m$ $2 m$ . If the object's angular velocity changes from $1 H z$ $1 Hz$ to $3 H z$ $3 Hz$ in $5 s$ $5 s$ , what torque was applied to the object?

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Answer 1 · 2016-01-04T17:00:19

$= 60.75 N . m$ $=60.75N.m$ .

Explanation:

From rotational dynamics we get that $\sum \to τ = I \to α$ $sumvectau=Ivecalpha$ , where $τ$ $tau$ is the torque, $I$ $I$ is the moment of inertia, and $α$ $alpha$ is the angular acceleration.

But since angular acceleration is the rate of change in angular velocity, we get that $α = \frac{d ω}{d t}$ $alpha=(domega)/(dt)$ .

We then first need to convert the linear frequency in Hertz into angular frequency in rad/s.

$α = \frac{d ω}{d t} = \frac{(3 \times 2 π r) - (1 \times 2 π r)}{5} = 5.0265 r a d / s^{2}$ $alpha=(domega)/(dt)=((3xx2pir)-(1xx2pir))/5=5.0265rad//s^2$ .

Moment of inertia $I = \sum j m_{j} r_{p e r p j}^{2} = \int_{m} r^{2} d m$ $I=sum_jm_jr_(perpj)^2=int_mr^2dm$ .

So in this case for a point mass, $I = m r^{2} = 3 \times 2^{2} = 12 k g . m^{2}$ $I=mr^2=3xx2^2=12kg.m^2$ .

Therefore resultant torque is $τ = I α$ $tau=I alpha$

$= 12 \times 5.0265$ $=12xx5.0265$

$= 60.75 N . m$ $=60.75N.m$ .

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An object with a mass of $3 k g$ $3 kg$ is traveling in a circular path of a radius of $2 m$ $2 m$ . If the object's angular velocity changes from $1 H z$ $1 Hz$ to $3 H z$ $3 Hz$ in $5 s$ $5 s$ , what torque was applied to the object?

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Explanation:

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An object with a mass of 3kg 3 kg is traveling in a circular path of a radius of 2m2 m. If the object's angular velocity changes from 1Hz 1 Hz to 3Hz 3 Hz in 5s 5 s, what torque was applied to the object?

1 Answer

Explanation:

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An object with a mass of $3 k g$ $3 kg$ is traveling in a circular path of a radius of $2 m$ $2 m$ . If the object's angular velocity changes from $1 H z$ $1 Hz$ to $3 H z$ $3 Hz$ in $5 s$ $5 s$ , what torque was applied to the object?