Question

An athlete can twirl a baton so that it reaches an angular velocity of 12 rad/s from rest in 0.5 s. If the length of a uniform baton is 0.8 m and the mass is 0.5 kg, what is the torque needed to reach the angular velocity? Group of answer choices

Answer 1

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

$F_c =ma_c= \frac{mv^2}{r} = m\omega^2 r$

Torque is given by;

$\tau = F_c *r\\\\\tau = m \omega^2 r *r\\\\\tau = m \omega^2 r^2 \\\\\tau = (0.5)(12)^2(0.8)^2\\\\\tau = 46.08 \ N m$

Therefore, the torque needed is 46.08 Nm