Answer:
The torque needed is 46.08 Nm
Explanation:
Given;
angular velocity, ω = 12 rad/s
time of motion, t = 0.5 s
length of the baton, r = 0.8 m
mass of the baton, 0.5 kg
The torque needed to reach the angular velocity is given by;
τ = F x r
where;
F is the centripetal force of the baton
r is the length of the baton = radius of the circular motion of the baton
[tex]F_c =ma_c= \frac{mv^2}{r} = m\omega^2 r[/tex]
Torque is given by;
[tex]\tau = F_c *r\\\\\tau = m \omega^2 r *r\\\\\tau = m \omega^2 r^2 \\\\\tau = (0.5)(12)^2(0.8)^2\\\\\tau = 46.08 \ N m[/tex]
Therefore, the torque needed is 46.08 Nm
