Question

A twirler’s baton is 0.76 m long and spins around its center. The end of the baton has a centripetal acceleration of 47.8 m/s2.

How long does it take the baton to complete one spin?

0.31 s
0.56 s
4.3 s
70 s

Answer 1

Radius r = 0.76/2 = 0.38 m.
a_c = ω^2 r ⇒ ω = sqrt(a_c / r) = sqrt(47.8 / 0.38) ≈ 11.21 rad/s.
Period T = 2π/ω ≈ 2π / 11.21 ≈ 0.56 s.

Answer: 0.56 s.