Engr Help

Angular Impulse/Momentum for Rigid Bodies in a Plane

Example: The figure below shows the top view of a bat OD (gravity is into the paper) of weight

W striking a baseball, R, of weight w. Assume the bat is a uniform bar of length L. The bat starts

in the dotted position and accelerates under the influence of a moment, M_o to the solid position

where the bat strikes the baseball, R, traveling initially at v_o = 60 mph. The coefficient of restitution

is e. The following data applies: L = 36 inches, M_o = 50 ft lb, W = 32 ounces, w = 5 ounces, θ = 30^o,

e = 0.8. Find the velocity of the baseball and the angular velocity of the bat immediately after impact.

Strategy:

First: Use Principle of Work and Energy to find the speed of the bat prior to impact.

Then for impact:

Step 1: Draw a free body diagram showing the impulse acting on the bat and on the baseball.

Step 2: Calculate the linear impulse and set it equal to the change in linear momentum

of the center of mass, C, of the bat.

Step 3: Calculate the angular impulse and set it equal to the change in angular momentum

of the bat.

Step 4: Calculate the linear impulse and set it equal to the change in linear momentum

of the baseball.

Step 5: Apply the definition of coefficient of restitution to relate normal velocities before

and after impact.

Hint: Use kinematics to relate linear and angular motion.