# Center of mass for high jumper

1. How is it that when high jumpers go over bars, their centers of mass pass underneath?

2. why must a hockey stick that is thrown rotating on ice stop rotating at exactly the same time as when the center of mass comes to rest?

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In order to get over the bar the person requires that all their mass should pass over the bar. This does not have to happen simultaneously.

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Is #2 even true? Can't you just spin the hockey stick so it has angular velocity but no translational velocity?

Chi Meson
Homework Helper
I just tried it with my ruler on the desktop. It is easy to slide it such that it keeps spinning after CM comes to rest. Is this really a homework question?

1) In the first case , when the athlete starts running , the c.m lies within the body and while the athlete is running , he experiences external forces of friction , thus the sentre of mass with accelerate/deccelerate along with the athlete , but when he loses his contact with the ground , there is an instantaneous absence of external forces and thus c.m keeps on travelling in same horizontal path even though athlete gains height , just like "in absence of external forces the c.m of a particle in projectile motion follows the same path even when the particle explodes and the pieces trace different paths.

2) "In absence of external forces , the c.m doesnot accellerate or changes its direction, the c.m in constant motion will remain in constant motion"

BJ

HallsofIvy
Homework Helper
Dr.Brain said:
1) In the first case , when the athlete starts running , the c.m lies within the body and while the athlete is running , he experiences external forces of friction , thus the sentre of mass with accelerate/deccelerate along with the athlete , but when he loses his contact with the ground , there is an instantaneous absence of external forces and thus c.m keeps on travelling in same horizontal path even though athlete gains height , just like "in absence of external forces the c.m of a particle in projectile motion follows the same path even when the particle explodes and the pieces trace different paths.
By the time the athlete loses contact with the ground, he had better have already established an upward component of velocity to his c.m. There certainly is not an "absence of external forces"- gravity is an external force. Ignoring air resistance, the jumper's c.m. follows a parabolic path, not a horizontal line. As others have said, the entire body does not have to pass over the the bar at the same time. Doing the "Fosbury Flop", the head and shoulders pass over the bar with the c.m not yet up to the bar. Then a swing of the arms and hips shifts the c.m. forward (with the c.m. going under the bar- the body is arched so that the c.m. lies inside the arch) so that the rest if the body can go over the bar. The "Western Roll" does something similar with one side of the body passing over the bar first. A hundred years ago, people were doing the "straddle jump"- where the center of mass does go over the bar and even olympic athletes could barely clear 5 feet.

2) "In absence of external forces , the c.m doesnot accellerate or changes its direction, the c.m in constant motion will remain in constant motion"
I don't see what this has to do with rotation. In any case the question necessarily assumes friction, an external force.

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physicsstudent12 said:
1. How is it that when high jumpers go over bars, their centers of mass pass underneath?

2. why must a hockey stick that is thrown rotating on ice stop rotating at exactly the same time as when the center of mass comes to rest?
To answer your second question, I think its because of the sticks shape. Due to the non uniformity of the stick, the centre of mass is not at the exact middle of the shaft, also, becuase of this, when the stick rotates on the ice about its centre of mass, it will have different frictional forces action on it on either side of the cm. These forces would cause the cm to move, threfore needing the rotation to be 0 when the cm is at rest. The ruler analogy does not work as a comparison to this becuase a ruler is uniform.

Regards,