A person swings a 0.33 kg tether ball tied to a 5.4 m rope in an approximately horizontal circle.

(a) If the maximum tension the rope can withstand before breaking is 11 N, what is the maximum angular speed of the ball?

Solve M R w^2 = Tmax.

to get w.

w = sqrt[Tmax/(M R)]

To find the maximum angular speed of the ball, we can start by considering the tension in the rope. When the ball is swinging in a horizontal circle, the tension in the rope is responsible for providing the centripetal force required to keep the ball moving in a circular path.

The centripetal force (F_c) is given by the equation:

F_c = (mass of the ball) * (angular speed)^2 * (radius of the circle)

In this case, the mass of the ball is 0.33 kg, the radius of the circle is 5.4 m, and we want to find the maximum angular speed.

Since the rope can withstand a maximum tension of 11 N before breaking, we can set the tension equal to the centripetal force:

Tension = F_c

11 N = (0.33 kg) * (angular speed)^2 * (5.4 m)

To find the maximum angular speed, we can rearrange this equation and solve for angular speed:

(angular speed)^2 = (11 N) / ((0.33 kg) * (5.4 m))

angular speed = √[(11 N) / ((0.33 kg) * (5.4 m))]

Calculating this, we find the maximum angular speed of the ball to be approximately 2.19 rad/s.