A carousel at a carnival has a diameter of 6.0 m. The ride starts from rest and accelerates at a constant angular acceleration to an angular speed of 0.7 rev/s in 8.8 s.
(a) What is the value of the angular acceleration?
1 0.499 rad/s^2
(b) What are the centripetal and angular accelerations of a seat on the carousel that is 2.40 m from the rotation axis?
ac =
á = 0.499 rad/s^2
I got angular accelaration correct but keep getting centripetal acceleration incorrect.....help!!
Given: 0.7rev/s, t = 8.8s, Dia. = 6.0m.
C = pi*D = 3.14*6 = 18.84m.
V = 0.7rev/s * 6.28rad/rev = 4.4rad/s.
a. (Vf - Vo) / t,
a = (4.4 - 0) / 8.8 = 0.5rad/s^2.
To find the centripetal acceleration of a seat on the carousel, you can use the formula:
ac = r * ω^2
where ac is the centripetal acceleration, r is the radius (distance from the rotation axis), and ω is the angular speed.
In this case, the radius (distance from the rotation axis) is given as 2.40 m, and the angular speed is given as 0.7 rev/s. However, we need to convert the angular speed to rad/s, since the formula requires angular speed in radian per second.
To convert from revolutions to radians, we use the conversion factor 2π radians = 1 revolution.
So, ω = 0.7 rev/s * 2π rad/rev = 1.4π rad/s
Now we can substitute the values into the formula:
ac = 2.40 m * (1.4π rad/s)^2
Calculating this expression will give you the centripetal acceleration of the seat on the carousel.