The Breakdown: The Accidental Gymnast
A moving sled and a static reporter make for one perfect expression of torque
This video provides a beautiful illustration of Newton’s Second Law in both its linear and angular form. The discombobulated newscaster experiences a linear acceleration in a backward direction, and a clockwise_angular_ acceleration that gets him spinning, all as a result of the force of the sled’s impact.
During contact the force is applied somewhere in the region of the reporter’s shins (ouch!). According to the Second Law in linear form (F = ma), this force gives him an acceleration in that direction while it is being applied. (In the absence of other forces, he would have continued moving backwards but at a constant speed.) If you watch the video carefully you can see that the newsman lands behind where he was standing before being launched. In fact, if it weren’t for gravity pulling him back to the ground he’d continue in that direction indefinitely.
Now what about that rotation? Because the force is applied low on his body, the reporter experiences a net clockwise torque around his center of mass (in this case, his stomach area) in addition to a net force backward. This causes an angular acceleration, or change in his rate of rotation.
A torque can be applied when a force acts away from an axis of rotation. For example, if the sled were to crash into the reporter’s stomach he would not experience a torque around his center and wouldn’t spin into a flip. If you’ve ever used a wrench you know that the farther a force is applied from an axis of rotation the more the torque around that axis. That shot to the shins is far enough from his center of mass to get him spinning pretty vigorously.
Newton’s Second Law in angular form (τ = Iα) relates the torque (τ) applied to an object to its resulting angular acceleration (α). In the case of rotation, the resistance to motion (or rotational inertia I) isn’t simply due to the mass, but also depends on the mass distribution. As any diver or gymnast knows, if the reporter could have pulled into a tuck position he would have lowered his rotational inertia, thus increasing his angular acceleration—and he might have been able to pull off a “double!”