A compact disc spins at 2.7 revolutions per second. An ant is walking on the CD and finds that it just begins to slide off the CD when it reaches a point 2.8 cm from the CD's center.
To find the acceleration of the ant, we need to determine the centripetal acceleration first.
The centripetal acceleration is given by the formula:
ac = ω^2 * r
where ac is the centripetal acceleration, ω is the angular velocity, and r is the radius.
Given:
ω = 2.7 revolutions per second, which can be converted to radians per second by multiplying by 2π (since 2π radians = 1 revolution).
So, ω = 2.7 * 2π = 16.98 rad/s
r = 2.8 cm = 0.028 m
Now, we can calculate the centripetal acceleration:
ac = (16.98 rad/s)^2 * 0.028 m
= 763.8648 m/s^2
Therefore, the centripetal acceleration of the ant is approximately 763.8648 m/s^2.