at a local country fair, the merry-go-round rotates at a rate of one circuit every 7.5 seconds. what is the angular velocity in radians per second
it makes 2PI radians per 7.5 sec
w= 2PI/7.5
To find the angular velocity in radians per second, you need to divide the angle the merry-go-round rotates by the time it takes to complete one circuit.
First, let's convert the angle to radians. One complete circuit is equal to 360 degrees or 2π radians.
Therefore, the angular velocity in radians per second can be calculated as:
Angular velocity (in radians per second) = Angle (in radians) / Time (in seconds)
Angle (in radians) = 2π radians
Time (in seconds) = 7.5 seconds
Angular velocity (in radians per second) = 2π radians / 7.5 seconds
Calculating the value:
Angular velocity (in radians per second) = 0.837 radians/second (rounded to three decimal places)
To find the angular velocity in radians per second, we need to know the relationship between the angle covered and the time taken.
Angular velocity is defined as the rate at which an object rotates, measured in radians per unit of time. In this case, we need to determine the number of radians covered in one second.
The formula to calculate angular velocity is:
Angular velocity (ω) = θ / t
Where:
ω = angular velocity in radians per second
θ = angle covered in radians
t = time taken in seconds
We know that the merry-go-round completes one circuit in 7.5 seconds. Since one circuit is equivalent to 360 degrees or 2π radians, we can use this information to find the angular velocity.
θ = 2π radians (angle covered)
t = 7.5 seconds (time taken)
Now we can substitute these values into the formula:
Angular velocity (ω) = θ / t
= 2π radians / 7.5 seconds
To simplify the calculation, we divide 2π by 7.5:
ω = 0.8378 radians/second (rounded to four decimal places)
Therefore, the angular velocity of the merry-go-round is approximately 0.8378 radians per second.