An object with a mass of  2 kg is traveling in a circular path of a radius of 7 m. If the object's angular velocity changes from  7 Hz to  9 Hz in  3 s, what torque was applied to the object?

Nov 1, 2017

410.7 Nm

Explanation:

$\text{Torque = Rate of change of Angular Momentum}$

$= \frac{{L}_{f} - {L}_{i}}{t}$

= (I ω_f - I ω_i) / t ………[∵ Angular Momentum = I ω]

= (I(ω_f - ω_i))/t

$= \frac{2 \pi I \left({f}_{f} - {f}_{i}\right)}{t}$ …………[∵ ω = 2pif]

$= \frac{2 \pi \times m {r}^{2} \left({f}_{f} - {f}_{i}\right)}{t}$

=(2xx22/7 × 2kg × (7 m)^2 × (9Hz - 7Hz))/(3s)

$= 410.7$ Nm