An object with a mass of $2 kg$ is traveling in a circular path of a radius of $4 m$ . If the object's angular velocity changes from $1 Hz$ to $9 Hz$ in $3 s$ , what torque was applied to the object?

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Answer 1 · 2016-01-02T16:23:41

Use basic rotational motion mechanics.

$τ=536.2 N*m$

The angular acceleration is:

$a=(Δω)/(Δt)$

$a=(9-1)/3 ((rounds)/s)/s$

$a=8/3 (rounds)/s^2$

Or in rads:

$a=8/3*2π$

$a=(16π)/3(rad)/s^2$

The moment of inertia of the object is:

$I=m*r^2$

$I=2*4^2 kg*m^2$

$I=32 kg*m^2$

Finally, the torque is calculated:

$τ=I*a$

$τ=32*(16π)/3 kg*m^2*1/s^2$

$τ=536.2 (kg*m/s^2)*m$

$τ=536.2 N*m$

An object with a mass of 2 kg 2 kg is traveling in a circular path of a radius of 4 m4 m. If the object's angular velocity changes from 1 Hz 1 Hz to 9 Hz 9 Hz in 3 s 3 s, what torque was applied to the object?