Question

Two students performed a shoulder press.

1st student had: an angular velocity of 80 degree/s going up and -36.21 degree/s going down.

2nd student had: an angular velocity of 46 degree/s going up and a -53.27 degree/s going down.

Why may the angular velocity of the first student be higher going up than the second student?

Why is the angular velocity of the 2nd student higher than the first student going down?

Why is angular velocity important?

Answer 1

(A) Shoulder press involves a lot of our upper arms. Let's imagine the lowest position in a shoulder press when the upper arm (from elbow to shoulder joint) is parallel to the floor. To push the weights up, the vertical forces need to be at least equal to the downward force of the weights. Both students will have to counteract the same forces. But, the angular velocity is given by,

where v is the tangential velocity and r is the position vector perpendicular to the velocity vector. So, higher the value of r lower the angular velocity. Hence, student 2 has a slower angular velocity because his shoulder to elbow distance is larger. So, he is probably taller than the first student.

(B) Now, consider the highest position of a shoulder press rep. The arms are not exactly perpendicular to the floor but the angle is quite large. At this point, the student with higher angular velocity in going up will have a slower angular velocity coming down. Why? During downward motion, the vertical component has to be opposing the gravitational weight but not enough to stop movement. We have already established that for the same tangential velocity, the longer arm will lead to slower angular velocity. Similarly, if both students have same tangential velocity downwards, the second student will oppose it a bit less than the first one, because of the longer arm which means that while coming down, the second student will have higher angular velocity.

(C) Angular velocity is important because it helps in the conservation of angular momentum. The perfect example is an ice skater spinning with his arms out. The relation with moment of inertia and angular momentum is.

Going back to the ice skater. When he spins with his arms out, the distribution of mass is spread out, which increases the moment of inertia. But, if with the same force he keeps spinning and midway tucks in his hands, the angular velocity will automatically increase without any external force. This is because when he tucks in his arms, the moment of inertia decreases. BUT ANGULAR MOMENTUM HAS TO BE CONSERVED. To compensate, the angular velocity of the skater will increase so the angular momentum does not change.