Calculate the angular velocity of the hour (not minute hand) hand of a clock in

Question

Calculate the angular velocity of the hour (not minute hand) hand of a clock in radians per second. Four 1.00 kg masses are bound into a square by four mass-less rigid rods that are 1.00 m long and form the sides of the square. Find the moment of inertia, I, of this object for rotation about each of the following axes. Perpendicular to plane of the object and through object through center-of-mass. Perpendicular to plane of the object and through one comer mass. In plane of the object and through center-of-mass, parallel to a rod. In plane of the object and along one of the rods.

Explanation / Answer

1)

angular velocity of hour hand is w = (2*pi)/T

period of the hour hand

then w = 2*3.142/(12 hour)

1 hour = 60*60 = 3600 sec

12 hour = 12*3600 = 43200

then w = 2*3.142/(43200) = 1.45*10^-4 rad/s

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2a)

I = 4*m*r^2 = 4*1*(0.5^2+0.5^2)= 2 kg-m^2

b) I = (2*m*r1^2)+(m*r2^2) = (2*1*1^2)+(1*2) = 4 kg-m^2

c) I = 4*m*r^2 = 4*1*0.5^2 = 1 kg-m^2

d) I = 2*m*r^2 = 2*1*1^2 = 2 kg-m^2

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