A coin sits 0.10m from the center of a
record player spinning at 45rpm.
a)
What is the frequency in Hertz?
b)
What is the period?
c)
What is the linear speed?
a) The frequency in Hertz can be calculated using the formula:
f = RPM/60
where RPM is rotations per minute. In this case, the RPM is given as 45 rpm, so:
f = 45/60 = 0.75 Hz
b) The period can be calculated using the formula:
T = 1/f
where f is the frequency we calculated in part (a). So:
T = 1/0.75 = 1.33 seconds
c) The linear speed of the coin can be calculated using the formula:
v = rω
where r is the distance from the center of the record player to the coin and ω is the angular velocity of the record player. The angular velocity can be calculated using the formula:
ω = 2πf
where f is the frequency we calculated in part (a). So:
ω = 2π(0.75) = 4.71 rad/s
Substituting the values we have:
v = 0.10m * 4.71 rad/s = 0.471m/s
So the linear speed of the coin is 0.471 m/s.
To answer these questions, we will use the following formulas:
a) Frequency (f) = Rotations per minute (RPM) / 60
b) Period (T) = 1 / Frequency (f)
c) Linear speed (v) = 2 * π * radius (r) * RPM / 60
Given:
Radius (r) = 0.10m
RPM = 45
a) To find the frequency in Hertz:
f = RPM / 60
f = 45 / 60
f = 0.75 Hz
Therefore, the frequency is 0.75 Hertz.
b) To find the period:
T = 1 / f
T = 1 / 0.75
T ≈ 1.33 seconds
Therefore, the period is approximately 1.33 seconds.
c) To find the linear speed:
v = 2 * π * r * RPM / 60
v = 2 * π * 0.10 * 45 / 60
v ≈ 0.942 m/s
Therefore, the linear speed is approximately 0.942 m/s.