Answer:
( Angular Velocity = ( About ) 230 rad / s,
( Linear Speed = ( About ) 40.25 m / s,
( Acceleration = ( About ) 9290 m / [tex]s^2[/tex]
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
_____
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
_____
And for this last bit here, to find the acceleration we can simply take the angular velocity ( omega ) squared, by the radius r -
( c ) [tex]a_{rad}[/tex] = w^2( r ),
[tex]a_{rad}[/tex] = ( ( 230 rad / sec )^2 )( .175 m )...
[tex]a_{rad}[/tex] = ( About ) 9290 m / [tex]s^2[/tex]
The angular velocity is 230 radian per second.
The linear speed is 40.25 m/s.
The acceleration is [tex]9257.5m/s^{2}[/tex]
It is given that, the diameter of wheel is 0.35 m.
So that, radius [tex]r=0.35/2=0.175m[/tex]
Since, One revolution is equal to [tex]2 \pi[/tex] radian.
So that,
[tex]w=2200rpm=\frac{2200*2\pi}{60} rad/s=230rad/s[/tex]
Thus, the angular velocity is 230 radian per second.
The linear speed v is computed as,
[tex]v=r*w\\\\v=(\frac{0.35}{2} )*230=40.25m/s[/tex]
The angular acceleration is calculated as;
[tex]a=\frac{v^{2} }{r} \\\\a=\frac{(40.25)^{2} }{0.175}=9257.5m/s^{2}[/tex]
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