Angular Velocity Calculation: Jack's Ride on a Merry-Go-Round

How can we determine Jack's angular velocity in radians per second?

Given that Jack climbs on a horse that is 12 feet from the center of a merry-go-round, and the merry-go-round makes 3.25 rotations per minute, what is Jack's angular velocity in radians per second?

Answer:

Jack's angular velocity is approximately 0.34 radians per second.

To determine Jack's angular velocity in radians per second, we need to follow a few steps. First, we convert the number of rotations per minute to rotations per second. Then, we use the angular velocity formula to calculate Jack's angular velocity.

Angular velocity is calculated using the formula: Angular velocity = (2π * Number of rotations) / Time

In this case, the merry-go-round makes 3.25 rotations per minute. To convert this to rotations per second, we divide 3.25 by 60, which equals 0.05417 rotations per second.

Now, we can plug this value into the formula: Angular velocity = (2π * 0.05417) / 1 = 0.3405 radians per second

Therefore, Jack's angular velocity is approximately 0.34 radians per second when rounded to the nearest hundredth.

Angular velocity is a crucial concept in physics, particularly when dealing with rotational motion. It represents the rate at which an object rotates around a specific axis, measured in radians per second. In Jack's case, understanding his angular velocity helps us determine how fast he is moving along with the merry-go-round.