The figure below shows a person about to kick a ball. To extend the lower leg and kick the ball, the
person only uses their quadriceps muscles (red arrow = force line of action), exerting a 2000N force.
The moment arm from muscle force to joint centre of rotation is 2.4cm. The moment of inertia of the
lower leg is 1.36kgm2. What is the angular acceleration of the lower leg as it kicks the ball?
To find the angular acceleration of the lower leg, we can use the principle of torque:
Torque = I * angular acceleration
First, let's calculate the torque generated by the quadriceps muscles:
Torque = Force * Moment Arm
Torque = 2000N * 0.024m
Torque = 48 Nm
Now, we can rearrange the torque equation to solve for angular acceleration:
angular acceleration = Torque / I
angular acceleration = 48 Nm / 1.36kgm^2
angular acceleration = 35.29 rad/s^2
Therefore, the angular acceleration of the lower leg as it kicks the ball is 35.29 rad/s^2.