Question

with what angular speed, in rad/s, does the earth rotate about its axis?
rad/s
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1. -/12.5 points

the triceps muscle in the back of the upper arm extends the forearm. this muscle in a professional boxer exerts a force of 2.00 × 10³ n with an effective perpendicular lever arm of 2.00 cm, producing
an angular acceleration of the forearm of 105 rad/s². what is the moment of inertia (in kg m²) of the boxers forearm?
kg m²

Explanation:

Step1: Recall the formula for angular speed

The formula for angular speed \(\omega=\frac{\Delta\theta}{\Delta t}\). For one full rotation of the Earth about its axis, \(\Delta\theta = 2\pi\) radians. The time period \(T\) (time for one full rotation) is approximately \(T = 24\space h\). Convert hours to seconds: \(T=24\times3600\space s = 86400\space s\).

Step2: Calculate the angular speed

Using \(\omega=\frac{2\pi}{T}\), substitute \(T = 86400\space s\). So \(\omega=\frac{2\pi}{86400}\space rad/s\approx7.27\times 10^{-5}\space rad/s\).

Answer:

\(7.27\times 10^{-5}\)