A helicopter blade spins at exactly 90 revolutions per minute. Its tip is $4.00 \mathrm{~m}$ from the center of rotation. (For each answer, enter a number.) (a) Calculate the average speed (in $\mathrm{m} / \mathrm{s}$ ) of the blade tip in the helicopter's frame of reference. $\mathrm{m} / \mathrm{s}$ (b) What is its average velocity (in $\mathrm{m} / \mathrm{s}$ ) over one revolution? $\mathrm{m} / \mathrm{s}$

Step 1 ：Given that the helicopter blade spins at exactly 90 revolutions per minute and its tip is 4.00 m from the center of rotation.

Step 2 ：First, we need to convert revolutions per minute to revolutions per second. This is done by dividing the given revolutions per minute by 60, since there are 60 seconds in a minute. So, \(\frac{90}{60} = 1.5\) revolutions per second.

Step 3 ：Next, we calculate the distance the blade tip travels in one revolution. This is the circumference of the circle it describes, which is given by the formula \(2\pi r\), where \(r\) is the radius (distance from the center of rotation to the tip of the blade). So, \(2\pi \times 4.00 = 25.13\) m.

Step 4 ：Then, we calculate the average speed of the blade tip by multiplying the distance per revolution by the number of revolutions per second. So, \(25.13 \times 1.5 = 37.7\) m/s.

Step 5 ：\(\boxed{\text{(a) The average speed of the blade tip in the helicopter's frame of reference is approximately 37.7 m/s.}}\)

Step 6 ：Finally, we calculate the average velocity of the blade tip over one revolution. Velocity is a vector quantity, which means it has both magnitude (speed) and direction. Over one revolution, the blade tip returns to its starting point, so the overall change in position is zero. Therefore, the average velocity is zero.

Step 7 ：\(\boxed{\text{(b) The average velocity of the blade tip over one revolution is 0 m/s.}}\)