Answer :
Answer:
t = 1.57 sec
distance, d = 98.65 mm
Step-by-step explanation:
Given an angle of 540°
At 6 revolutions per second, which is the angular velocity.
Radius, r = 10 mm
We are asked to find the time and the distance.
To find the time, let's use the formula:
[tex] \theta = a*t [/tex]
Where [tex] \theta [/tex] = angle in radians.
Converting 540° to radians, we have:
[tex] \theta = 540 * \frac{\pi}{180} = 9.42 rad [/tex]
Therefore, from the formula, let's find t.
[tex] \theta = a*t [/tex]
[tex]9.42 = 6 * t[/tex]
[tex]t = \frac{9.42}{6} = 1.57[/tex]
time = 1.57
To find the distance, we have:
[tex] \frac{1.57 * 360}{360} = \frac{d}{2 \pi r} [/tex]
[tex] \frac{1.57 * 360}{360} = \frac{d}{2\pi 10} [/tex]
[tex] 1.57 = \frac{d}{20\pi} [/tex]
[tex] d = 20 \pi *1.57 [/tex]
d = 98.65 mm
Therefore, the time is 1.57 seconds and the distance is 98.65 mm