the road? What is the minimum coefficient of static friction required to keep the car in this turn? 6. A rotating fan completes 1200 revolutions every minute .Consider a point on the tip of a blade,at a radius of 015 m. (a)through what linear distance does the point move in one revolution? (b)What is the linear speed of the point? 7. The four particles in figure below are connected by rigid rods of negligible mass.The origin is at the center of the rectangle. If the system rotates in the xy plane about the z axis with an angular speed of 6.00rad/s calculate (a)the moment of inertia of the system about the zaxis and (b) the rotational kinetic energy of the system.

## Step 1: Linear Distance CalculationTo calculate the linear distance a point on the tip of a blade moves in one revolution, we use the formula for the circumference of a circle, which is given by , where is the radius of the circle. In this case, the radius is the length of the blade, which is 0.15 m. ### m## Step 2: Linear Speed CalculationThe linear speed of the point can be calculated using the formula , where is the distance traveled and is the time taken. In this case, the distance is the circumference of the circle (0.94 m) and the time is the time taken for one revolution. Since the fan completes 1200 revolutions every minute, the time for one revolution is minutes or seconds.### \(v = d/t = 0.94 / (1/20) = 18.8\) m/s## Step 3: Moment of Inertia CalculationThe moment of inertia of the system about the z-axis can be calculated using the formula , where is the mass of each particle and is the distance of each particle from the axis of rotation. In this case, since the origin is at the center of the rectangle, the distance of each particle from the z-axis is the same and is equal to the half of the length of the rectangle. Let's denote this distance as . The total moment of inertia is then the sum of the moments of inertia of all four particles.### ## Step 4: Rotational Kinetic Energy CalculationThe rotational kinetic energy of the system can be calculated using the formula , where is the moment of inertia and is the angular speed. In this case, the angular speed is given as 6.00 rad/s.### \(K = \frac{1}{2} I \omega^2 = \frac{1}{2} \times 4 m r^2 \times (6.00)^2\)