The Earth rotates on it's axis once every 24 hours.
a)How long does it take Earth to rotate through an angle of 4pi/3?
b)How long does it take Earth to rotate through an angle of 210 degrees?
time= displacement/angular speed=(4PI/3)/(2PIrad/24hrs)=4PI*24/6PI==16hrs
a) To find the time it takes for Earth to rotate through an angle of 4π/3, we can use the formula:
Time = (Angle)/(Angular Velocity)
The Earth completes one full rotation in 24 hours, which is equivalent to 2π radians. Therefore, the angular velocity can be calculated as:
Angular Velocity = (2π radians) / (24 hours)
Now, we can substitute the values into the formula:
Time = (4π/3) / [(2π radians) / (24 hours)]
simplifying the equation:
Time = (4π/3) * (24 hours) / (2π radians)
Time = (4/3) * (24 hours) / 2
simplifying further:
Time = (4/3) * 12 hours
Time = 16 hours
Therefore, it takes Earth 16 hours to rotate through an angle of 4π/3.
b) To find the time it takes for Earth to rotate through an angle of 210 degrees, we can use the same formula:
Time = (Angle)/(Angular Velocity)
First, let's convert 210 degrees into radians:
Angle (in radians) = (210 degrees) * (π/180 degrees)
Angle = (210π/180) radians
The angular velocity is the same as in part a):
Angular Velocity = (2π radians) / (24 hours)
Now, we can substitute the values into the formula:
Time = (210π/180) / [(2π radians) / (24 hours)]
simplifying the equation:
Time = (210π/180) * (24 hours) / (2π radians)
simplifying further:
Time = (7/6) * (4 hours)
Time = 7 hours
Therefore, it takes Earth 7 hours to rotate through an angle of 210 degrees.
To answer these questions, we need to know the relationship between angles and time.
a) To calculate the time it takes for Earth to rotate through an angle of 4π/3, we can use the formula:
Time = (Angle / 2π) * 24 hours
In this case, the angle is 4π/3:
Time = (4π/3 / 2π) * 24 hours
Simplifying the fraction:
Time = (2/3) * 24 hours
Therefore, it takes Earth 16 hours to rotate through an angle of 4π/3.
b) To calculate the time it takes for Earth to rotate through an angle of 210 degrees, we can use the same formula:
Time = (Angle / 360) * 24 hours
In this case, the angle is 210 degrees:
Time = (210 / 360) * 24 hours
Simplifying the fraction:
Time = (7/12) * 24 hours
Therefore, it takes Earth 14 hours to rotate through an angle of 210 degrees.