A point on a wheel rotating at 5revs/s is located 0.20m away from the axis. What is the centripetal acceleration?
a. 198m/s^2
b. .05m/s^2
c. 48m/s^2
d. 1.35m/s^2
a=v^2/r=(10pi r/1)^2 / r
a= 100PI^2 r
To find the centripetal acceleration, we can use the formula:
ac = rω^2
where ac is the centripetal acceleration, r is the distance from the axis, and ω is the angular velocity.
In this case, we have:
r = 0.20m (distance from the axis)
ω = 5revs/s (angular velocity)
Plugging these values into the formula, we get:
ac = (0.20m) * (5revs/s)^2
Now, we need to convert the angular velocity from revolutions per second (revs/s) to radians per second (rad/s). Since there are 2π radians in one revolution, we can multiply the angular velocity by 2π to convert it:
ω = 5revs/s * 2π rad/rev = 10π rad/s
Plugging this value into the formula, we get:
ac = (0.20m) * (10π rad/s)^2
Now we can simplify the expression:
ac ≈ 19.739 m/s^2
Rounded to two decimal places, the answer is approximately 19.74 m/s^2.
Since none of the given options match this value exactly, it seems there may be a mistake in the provided answer choices.