Why longer arms allow you to throw further

[clurt]

Or how golf clubs are long and allow you to hit the ball far.

Please explain in physics terms, is it to do with torque? A few sentences is plenty(or more if you don't mind).

Thanks

 

[jbriggs444]

There is a limit on how fast you can effectively move your legs, arms, hands and feet. The faster you move them, the more effort goes into just waving your hands or pumping your legs and the less is available to go into the object you are throwing or the thrust with which you are running.

A lever allows you to push harder while moving more slowly.

That's one reason a golf club or a mace works better than a ball or a rock in your hand. It's also a reason why a racing scull has long oars and why a bicycle has gears.

A bow/arrow and a sling/stone achieve a similar result with a different mechanism. In both cases you use a slow effort to generate a fast effect.

There are other effects at work in a golf club. But you asked about length.

 

[0xDEADBEEF]

Just to make clear what jbriggs444 said. A club is the inverse of a lever, you need more force to swing it, but the tip is much faster, and that is all that counts because the head of the club can accelerate over a long path and will have a lot of speed / kinetic energy to transfer to the ball.

 

[94JZA80]

the short answer is velocity - the higher an object's velocity is when it is released, the farther it will travel (assuming you give it the right trajectory).

imagine a rotating disk 4m in diameter. its circumference is 2∏r = 2(3.14)(2) = 12.56m. so if it rotates at 1rpm, any given point on the edge of the disk will travel 12.56 meters in one minute. now imagine a rotating disk only 2m in diameter. its circumference is 2∏r = 2(3.14)(1) = 6.28m. at 1rpm, any given point on this disk's edge will travel 6.28 meters in one minute. note that such a point only travels half the distance in a given time period as any point on the larger rotating disk travels in that same time period. therefore any point on the larger disk's edge must travel at twice the velocity as any point on the smaller disk's edge in order to cover twice the distance in the same amount of time.

now alter your mental picture a bit - place a 2m rod on the 4m diameter disk such that one end is at the center of the disk and the other end falls on any point at the disks edge. now treat the rod as a lever and the center of the disk as a fulcrum, and you'll see how the system has the same mechanics as an arm throwing a ball (where the shoulder is the fulcrum and the arm is the lever) or legs running (where the hip would be the fulcrum and the legs are the levers). in summary, if levers of various lengths are translated about a fulcrum through the same exact angle and at the same exact speed of rotation, the tip of the longest lever will have the greatest velocity, and therefore will have the potential to launch an object farther than any of the other levers.