The Olympic diver completes 3.5 somersaults in 1.7 seconds. What is the average angular speed (in rad/s) of the diver?
One somersault is a complete circle, namely 2π radians. So 3.5 somersaults in 1.7 s would be equivalent to 3.5*2π/1.7 radians/s.
12.9
Why did the Olympic diver bring a calculator to practice? Because they wanted to make sure they didn't make any "sine" mistakes!
Now, let's calculate the average angular speed of the diver. We know that the number of somersaults is related to the angle covered, and since one complete somersault is equal to 2π radians, the diver completes 3.5 * 2π radians.
To find the average angular speed, we divide the angle (3.5 * 2π) by the time (1.7 seconds).
So, grab your diving gear, make sure you're not "triangulated" and let's crunch the numbers:
Average angular speed = (3.5 * 2π radians) / (1.7 seconds)
Just remember to always "dive" into math with a smile!
To find the average angular speed of the diver, we need to determine the number of complete revolutions made by the diver and the time taken.
1 revolution = 2π radians
The number of revolutions made by the diver can be calculated by dividing the number of somersaults by 2 since each somersault is equal to one revolution.
Number of revolutions = 3.5 somersaults / 2 = 1.75 revolutions
Next, we need to convert the time taken into seconds.
Time taken = 1.7 seconds
Now, we can calculate the average angular speed by dividing the number of revolutions by the time taken.
Average angular speed = Number of revolutions / Time taken
= 1.75 revolutions / 1.7 seconds
Therefore, the average angular speed of the diver is 1.0294 radians per second (rounded to four decimal places).
To find the average angular speed, we need to divide the total angular displacement by the time taken.
Angular displacement is the total angle covered in the given time. In this case, the diver completes 3.5 somersaults, which means they complete 3.5 * 360 degrees of rotation.
To convert degrees to radians, remember that 1 degree is equal to π/180 radians. So, we can calculate the total angular displacement in radians by multiplying by the conversion factor: (3.5 * 360 degrees) * (π/180 radians per degree).
Next, we divide the total angular displacement by the time taken. In this case, the time taken is 1.7 seconds.
Finally, we can calculate the average angular speed by dividing the total angular displacement by the time taken.
Let's plug in the numbers: