Answer:
( Angular Velocity = ( About ) 230 rad / s,
( Linear Speed = ( About ) 40.25 m / s,
( Acceleration = ( About ) 9290 m /
Explanation:
Here we want the angular velocity in radians per second, the linear velocity and acceleration.
The diameter = .35 meters, and thus we can conclude that the radius be half of that, or .175 meters. For part ( a ), or the calculation of the angular velocity, it is given that the diameter rotates at 2200 revolutions per minute - but we need to convert this into radians per second.
We can say that there are 2π radians for every minute, and for every minute there are 60 seconds. Therefore -
( a ) w = 2,200 rpm( 2π rads / rev )( 1 min / 60 sec )...
Hence, w = ( About ) 230 rad / s
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For this second part we can calculate the the linear velocity by multiplying the angular velocity ( omega ) by the radius r -
( b ) v = w( r ) - Substitute,
v = ( 230 rad / sec )( .175 m )...
v = ( About ) 40.25 m / s
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And for this last bit here, to find the acceleration we can simply take the angular velocity ( omega ) squared, by the radius r -
( c ) = w^2( r ),
= ( ( 230 rad / sec )^2 )( .175 m )...
= ( About ) 9290 m /