An object moves in a circular path at 861 rpm. If the radius of its circular path is 9.27 meters, calculate
a) the distance traveled in one complete revolution
d = m
b) the time it takes for one complete revolution
T = seconds
c) the linear speed of the object as it moves in a circular path
v = m/s.
a. d = Circumference = pi*2r = 3.14 * 18.54 = 58.25 m.
b. T = 1min/861rev = 60s/861rev = 0.0697 s./rev
c. V=861rev/min * 58.25m/rev * 1min/60s
=
To solve these questions, we need to understand some basic concepts related to circular motion.
a) The distance traveled in one complete revolution is equal to the circumference of the circular path. The formula for the circumference of a circle is C = 2πr, where r is the radius.
In this case, the radius of the circular path is given as 9.27 meters. Therefore, the distance traveled in one complete revolution can be calculated as:
d = 2π * 9.27 meters
b) The time it takes for one complete revolution is also known as the period of revolution. It can be calculated using the formula T = 1/f, where f is the frequency of revolution. Frequency is the number of revolutions per unit of time.
In this case, the frequency of revolution is given as 861 rpm (revolutions per minute). To find the period of revolution in seconds, we need to convert minutes to seconds because the SI unit of time is seconds.
T = 1 / (861 rpm) * (1 min / 60 sec)
c) The linear speed of the object is the distance traveled per unit of time. It can be calculated using the formula v = d / T, where d is the distance traveled in one complete revolution and T is the time for one complete revolution.
In this case, we already calculated the distance (d) in part a) and the time (T) in part b). So, we can substitute these values into the formula to find the linear speed.
Now we can calculate the answers:
a) The distance traveled in one complete revolution:
d = 2π * 9.27 meters ≈ 58.22 meters
b) The time it takes for one complete revolution:
T = 1 / (861 rpm) * (1 min / 60 sec) ≈ 0.007 seconds
c) The linear speed of the object:
v = 58.22 meters / 0.007 seconds ≈ 8317.14 m/s