For a record playing at 45 rpm, find the frequency and the angular velocity.
Frequency=
Angular velocity=
F = 45rev/min = 45rev/60s = 0.75rev/s = 0.75c/s = 0.75 Hz.
Va=45rev/min * 6.28rad/rev * 1min/60s =
4.71 Rad/s.
To find the frequency and angular velocity of a record playing at 45 rpm, we need to understand the relationship between rpm and frequency/angular velocity.
1. Frequency:
Frequency is the number of complete cycles (or revolutions) per unit of time. In this case, we are given the rpm (revolutions per minute) and we want to find the frequency in Hz (hertz).
To convert rpm to frequency in Hz, we can use the following formula:
Frequency (in Hz) = rpm / 60
So, for a record playing at 45 rpm, the frequency would be:
Frequency = 45 rpm / 60 = 0.75 Hz
2. Angular velocity:
Angular velocity represents the rate of change of angular displacement for rotating objects. It is usually measured in radians per second (rad/s).
To convert rpm to angular velocity in rad/s, we can use the following formula:
Angular velocity (in rad/s) = 2 * π * (rpm / 60)
So, for a record playing at 45 rpm, the angular velocity would be:
Angular velocity = 2 * π * (45 / 60) = 4.71 rad/s
Therefore, for a record playing at 45 rpm, the frequency is 0.75 Hz and the angular velocity is 4.71 rad/s.
To find the frequency and angular velocity of a record playing at 45 rpm, we can follow these steps:
1. Convert the rpm value to revolutions per second (rps):
- Divide the rpm value by 60 to convert it to revolutions per minute (r/min).
- Divide the result by 60 to convert it to revolutions per second (r/s).
Let's apply this formula:
rps = 45 rpm / 60
rps = 0.75 r/s
2. Convert the revolutions per second to frequency:
- Frequency is defined as the number of complete cycles or revolutions per second.
Let's use this formula:
frequency = rps * 2π
Note: 2π is the conversion factor between angular velocity and frequency.
frequency = 0.75 r/s * 2π
frequency ≈ 4.71 Hz
3. Calculate the angular velocity:
- Angular velocity represents how fast an object rotates around a specific axis.
Let's apply this formula:
angular velocity = rps * 2π
angular velocity = 0.75 r/s * 2π
angular velocity ≈ 4.71 rad/s
Therefore, for a record playing at 45 rpm:
- The frequency is approximately 4.71 Hz.
- The angular velocity is approximately 4.71 rad/s.