A coin is placed on a stereo record revolving at 33 1/3 revolutions per minute.
(b) Find the acceleration of the coin when it is placed 5.0, 10, and 15 cm from the center of the record.
2 ____ . m/s2 (5.0 cm)
3 ____ . m/s2 (10 cm)
4 ____ . m/s2 (15 cm)(c) What force accelerates the coin?
To find the acceleration of the coin placed at different distances from the center of the record, we will need to use the formula for centripetal acceleration:
a = rω^2
where:
a is the acceleration,
r is the radius from the center of rotation, and
ω (omega) is the angular velocity.
First, let's find the angular velocity (ω) in radians per second:
The stereo record makes 33 1/3 revolutions per minute. There are 60 seconds in a minute, so the record makes (33 1/3) / 60 revolutions per second.
Next, we need to convert revolutions to radians. Since one revolution is equivalent to 2π radians, we can calculate ω by multiplying the number of revolutions per second by 2π:
ω = (33 1/3) / 60 * 2π
Now we can calculate the acceleration for the different distances:
For 5.0 cm from the center:
a = (0.05 m) * (ω^2)
For 10 cm from the center:
a = (0.10 m) * (ω^2)
For 15 cm from the center:
a = (0.15 m) * (ω^2)
To find the force accelerating the coin, we can use Newton's second law of motion:
F = m * a
where:
F is the force,
m is the mass of the coin, and
a is the acceleration.
Assuming the mass of the coin is given, you can easily find the force by multiplying the mass by the corresponding acceleration.
It is important to note that the above calculations assume a constant angular velocity throughout the entire rotation of the record. In reality, the angular velocity might not remain perfectly constant due to various factors like friction and imperfections in the record.