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 1<br />Tangential 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.<br /><br />## Step 2<br />The formula for tangential velocity is given by:<br />### \(v = \frac{2\pi r}{T}\)<br />where \(v\) is the tangential velocity, \(r\) is the radius of the circle, and \(T\) is the time taken to complete one revolution.<br /><br />## Step 3<br />In this problem, the time \(T\) 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.<br /><br />## Step 4<br />Substituting the values of the radius into the formula, we get:<br />For the 2m hoop, \(v = \frac{2\pi \times 1}{2} = \pi\) m/s<br />For the 4m hoop, \(v = \frac{2\pi \times 2}{2} = 2\pi\) m/s<br /><br />## Step 5<br />Comparing 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.