a coin is placed on a stereo revolving at 33.3 revolutions per minute. what is its centripetal acceleration when it is placed 5 cm from the center of the turntable?
To find the centripetal acceleration of a coin placed on a revolving stereo turntable, we can use the formula for centripetal acceleration:
a = r * ω^2
where:
a = centripetal acceleration
r = distance from the center of the turntable to the coin
ω = angular velocity
First, let's convert the given linear velocity of the turntable into angular velocity:
ω = 2πf
where:
f = frequency of rotation
Given that the turntable is revolving at 33.3 revolutions per minute, we can convert this to frequency (f) in Hz:
f = 33.3 rev/min * (1 min/60 s) = 0.555 Hz
Now, we can calculate the angular velocity (ω):
ω = 2π * 0.555 = 3.49 rad/s
Next, substitute the given distance (r = 5 cm = 0.05 m) and angular velocity (ω) into the centripetal acceleration formula:
a = 0.05 m * (3.49 rad/s)^2
Simplifying the equation:
a ≈ 0.05 m * 12.19 m^2/s^2
a ≈ 0.61 m/s^2
Therefore, the centripetal acceleration of the coin when it is placed 5 cm from the center of the turntable is approximately 0.61 m/s^2.