Julia is using two hoops to test tangential velocity. As she spins a ball within the two hoops, she wonders which ball has the faster tangential velocity The two hoops are 2 m in diameter and 4 m in diameter. Which hoop would provide the greatest tangential velocity if they complete the circle in 2 seconds? They would be equal. 4 m hoop Not enough information to determine. 2 m hoop

## Step 1Tangential velocity is the linear speed of an object moving along a path. It is the speed of the object at any given point on the path. In this case, the path is a circle, and the object is a ball spinning within two hoops.## Step 2The formula for tangential velocity is given by:### where is the tangential velocity, is the radius of the circle, and is the time taken to complete one revolution.## Step 3In this problem, the time is the same for both hoops, which is 2 seconds. The radius of the hoops is half of their diameter. Therefore, the radius of the 2m hoop is 1m, and the radius of the 4m hoop is 2m.## Step 4Substituting the values of the radius into the formula, we get:For the 2m hoop, m/sFor the 4m hoop, m/s## Step 5Comparing the two velocities, we can see that the velocity of the ball in the 4m hoop is twice that of the ball in the 2m hoop. Therefore, the ball in the 4m hoop has a greater tangential velocity.