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

Question

2009 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-03T11:04:31

The torque is $= 150.8 N m$ $=150.8Nm$

The torque is the rate of change of angular momentum

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

The moment of inertia of the object is $I = m r^{2}$ $I=mr^2$

$= 2 \cdot 2^{2} = 8 k g m^{2}$ $=2*2^2= 8 kgm^2$

The rate of change of angular velocity is

$\frac{d ω}{d t} = \frac{4 - 1}{1} \cdot 2 π$ $(domega)/dt=(4-1)/1*2pi$

$= (6 π) r a d s^{- 2}$ $=(6pi) rads^(-2)$

So the torque is $τ = 8 \cdot (6 π) N m = 48 π N m = 150.8 N m$ $tau=8*(6pi) Nm= 48piNm=150.8Nm$

An object with a mass of 2 kg2kg 2 kg is traveling in a circular path of a radius of 2 m2m2 m. If the object's angular speed changes from 1 Hz1Hz 1 Hz to 4 Hz4Hz 4 Hz in 1 s1s 1 s, what torque was applied to the object?