# An object with a mass of  8 kg is traveling in a circular path of a radius of 12 m. If the object's angular velocity changes from  15 Hz to  7 Hz in  6 s, what torque was applied to the object?

Jan 31, 2016

Torque=-803.52 Newton.meter

#### Explanation:

${f}_{1} = 15 H z$
${f}_{2} = 7 H z$
${w}_{1} = 2 \cdot 3.14 \cdot 15 = 30 \cdot 3.14 = 94.2 \frac{r a d}{s}$
${w}_{2} = 2 \cdot 3.14 \cdot 7 = 14 \cdot 3.13 = 43.96 \frac{r a d}{s}$
$a = \frac{{w}_{2} - {w}_{1}}{t}$
$a = \frac{43.96 - 94.2}{6}$
$a = - 8.37 \frac{m}{s} ^ 2$
$F = m \cdot a$
$F = - 8 \cdot 8.37 = - 66.96 N$
$M = F \cdot r$
$M = - 66.96 \cdot 12 = - 803.52$ , Newton.meter