Suppose a 0120kg ball is thrown at 120 ms to a motionless pe

Suppose a 0.120-kg ball is thrown at 12.0 m/s to a motionless person standing on ice who catches it with an outstretched arm as shown in the figure below.

(a) Calculate the final linear velocity of the person, given his mass is 88.0 kg.
m/s
(b) What is his angular velocity if each arm is 6.00 kg? You may treat the ball as a point mass and treat the person\'s arms as uniform rods (each has a length of0.870 m) and the rest of his body as a uniform cylinder of radius 0.160 m. Neglect the effect of the ball on his center of mass so that his center of mass remains in his geometrical center.
  rad/s

Solution

m = 0.120 Kg

u = 12 m/s

a) let the final linear speed of the person is v

Using conseravtion of momentum

0.120 * 12 = (88 + 0.12) * v

v = 0.0163 m/s

the final linear velocity of the person is 0.0163 m/s

b)

let the angular speed is w

(2 * (1/3) * 6 * 0.87^2 + (88 -12) * 0.16^2 * 0.5 + 0.12 * ) * w = 0.120 * 12 * (0.87 + 0.16)

solving for w

w = 0.370 rad/s

the angular speed of the body is 0.370 rad/s