A square plate with sides 2.2 m in length can rotate around an axle passing thro

Question

A square plate with sides 2.2 m in length can rotate around an axle passing through its center of mass (CM) and perpendicular to its surface (see figure below). There are four forces acting on the plate at different points. The rotational inertia of the plate is

32 kg · m2.

Use the values given in the figure to answer the following questions. Assume the plate starts from rest. (Assume = 48°.)

(a) What is the angular velocity of the plate after 4.0 s? (Express your answer in vector form.)

(b) Through how many revolutions will the plate rotate in 4.0 s?

Explanation / Answer

balancing moment

30*1.1+20*1.1+60*1.1-(40sin48)*1.1-(40cos48)*1.1=32*w

w=58.86/32=1.84rad/s

b)rad=4*1.84=7.36 rad

2(pi) rev=1 rad

rev=7.36/(2(pi))=1.1776 rev

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