An old-fashioned single-play vinyl record rotates on a turntable at 34.0rpm .
What are the angular velocity in rad/s and the period of the motion?
(34 rev/min)x(2 pi rad/rev)x(1 min/60s)
= ? rad/s
P = 1/f, so the period P is 1/34 minute.
Multiply that by 60 s/min if you want it in seconds
To find the angular velocity in rad/s, you can use the following formula:
Angular velocity (ω) = 2π × Frequency
To convert rpm (revolutions per minute) to frequency (revolutions per second), divide by 60:
Frequency = 34.0 rpm / 60 s/min
Now let's calculate the angular velocity:
Angular velocity (ω) = 2π × (34.0 rpm / 60 s/min)
To find the period of the motion, you can use the following formula:
Period (T) = 1 / Frequency
Now let's calculate the period:
Period (T) = 1 / (34.0 rpm / 60 s/min)
Please note that both angular velocity and period depend on the units you prefer.
To determine the angular velocity in rad/s and the period of the motion, you need to understand the relationship between rotation speed (given in rpm) and angular velocity (in rad/s).
1. Angular Velocity (ω):
Angular velocity is the rate at which an object rotates, measured in radians per second (rad/s). It can be calculated using the following formula:
ω = 2πf
Where:
- ω is the angular velocity in rad/s.
- f is the frequency of rotation in Hz (Hertz).
2. Period (T):
Period is the time it takes for one complete revolution or cycle to occur. It is the reciprocal of frequency (T = 1/f). In this case, since we have the rotation speed in rpm, we'll have to convert it into frequency in Hz using the following formula:
f = rpm / 60
Where:
- f is the frequency of rotation in Hz.
- rpm is the rotation speed in revolutions per minute.
Now, let's apply these formulas to the given information:
Given:
- Rotation speed (rpm) = 34.0
Step 1: Convert rotation speed to frequency (f):
f = rpm / 60
f = 34.0 / 60
f ≈ 0.5667 Hz
Step 2: Calculate angular velocity (ω):
ω = 2πf
ω = 2π * 0.5667
ω ≈ 3.56 rad/s
Therefore, the angular velocity of the vinyl record is approximately 3.56 rad/s, and the period of the motion is approximately 1.766 seconds (calculated as reciprocal of 0.5667 Hz).