An athletic 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 of length L and mass M rotating about its center is:

I = (1/12)ML^2

Using this moment of inertia, we can calculate the torque required to reach the angular velocity:

τ = Iα = (1/12)ML^2(ωf - ωi)/t

where ωi = 0 is the initial angular velocity.

Plugging in the given values, we get:

τ = (1/12)(0.5 kg)(0.8 m)^2(12 rad/s)/0.5 s

τ = 0.64 Nm

Therefore, the answer is D) 0.64 Nm.

An Athletic Can Twirl a Baton So That It Reaches