the Moon orbits Earth every 27.3 days. Determine the angular velocity of the moon in degrees per day and in radian per day
2πrad/27.3day = ____ rad/day
To determine the angular velocity of the moon in degrees per day, we need to find how many degrees the moon travels in one day.
We know that the moon orbits Earth in 27.3 days. In one day, it covers 360 degrees.
Therefore, the angular velocity of the moon in degrees per day is:
Angular velocity (in degrees per day) = 360 degrees / 27.3 days ≈ 13.186 degrees per day.
To determine the angular velocity of the moon in radians per day, we need to convert the degree measurements to radians.
Since there are 2π radians in a full circle (360 degrees), we can use the conversion factor:
1 degree = π/180 radians
So the angular velocity of the moon in radians per day is:
Angular velocity (in radians per day) = 13.186 degrees per day * (π/180 radians per degree) ≈ 0.229 radians per day.
To determine the angular velocity of the Moon in degrees per day and radian per day, we need to use the formula:
Angular velocity = 2π / Time period
First, let's determine the angular velocity in degrees per day:
Angular velocity in degrees per day = 2π / Time period
Time period = 27.3 days
Angular velocity in degrees per day = 2π / 27.3
To calculate the value, we divide 2π (approximately 6.28319) by 27.3:
Angular velocity in degrees per day ≈ 0.229 degrees per day
Now, let's convert this angular velocity to radians per day:
To convert degrees to radians, we use the following conversion factor:
1 radian = 180 degrees / π
Angular velocity in radians per day = (Angular velocity in degrees per day) * (π / 180)
Substituting the value we obtained:
Angular velocity in radians per day ≈ 0.229 * (π / 180)
Simplifying the equation:
Angular velocity in radians per day ≈ 0.004 radians per day
Therefore, the Moon's angular velocity is approximately 0.229 degrees per day and 0.004 radians per day.