Answer :
a = 23.6 The speed b = 1.64 magnitude of the average velocity
16R/s is the frequency, and 0.47 m0.47m is the diameter. Hence:
16R/s=f= 1/T
and
d = 0.47m = 2r , r=d/2= 0.235
So we can solve for the period (T)
16Rs-¹= f = 1/T
1/16 = T
Then, we have to remember that, in a uniform circular motion, the centripetal acceleration is given by
a = v²/r = 4π²r/T²
Now we have to substitute.
a = 4π²(0.235)/(1/16)²
a=2375.02ms-²
Then, we can use the equation
a = v²/r to solve v
2375.02 = v²/r
2375.02 = v²/0.235
(0.235) (2375.02) = v²
√(0.235)(2375.02) = v
23.6 = v
(B) 3.25 revolutions means that the displacement will be 0.25 or 1/4 of the circumference.
Hence, the displacement becomes the hypotenuse in a right triangle is where we can use the Pythagorean theorem.
a=b=r
a=b=0.235
a²+b²=c²
(0.235)² + (0.235)² = c²
C = 0.47/√2
The total time for 3.25 revolutions has to be equal to
3.25T = (3.25) (1/16)
So, since the average velocity is
Displacement/Time we can input the values we have and solve for the result.
Displacement/time = Va
0.47√2 / (3.25) (1/16)
1.64ms-¹ = Va
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