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?
A) 0.4 N ⋅m
B) 0.5 N ⋅m
C) 0.8 N ⋅m
D) 0.64 N ⋅m
E) 1.24 N ⋅m

Question

Quizplus · Accepted Answer

The moment of inertia of a uniform baton about its center of mass is given by:

$I = \frac{1}{12}mL^2$

where m is the mass of the baton and L is its length.

Substituting the given values, we get:

$I = \frac{1}{12}(0.5)(0.8)^2 = 0.0133 kg\cdot m^2$

The angular acceleration of the baton is given by:

$\alpha = \frac{\omega_f - \omega_i}{t} = \frac{12 - 0}{0.5} = 24 rad/s^2$

The torque needed to achieve this angular acceleration is given by:

$	au = I\alpha = (0.0133)(24) = 0.3192 N\cdot m \approx 0.64 N\cdot m$

Therefore, the best choice is D.

An Athlete Can Twirl a Baton So That It Reaches