Peoples Physics Concepts

9.5 Yo-Yo Type Problems

9.5 Yo-Yo Type Problems

• Solve Yo-Yo type problems, where an object is rotating in free fall yet attached to a string (or some other
  similar restraint).

Students will learn to solve Yo-Yo type problems. That is problems where an object is rotating in free fall yet

attached to a string (or some other similar restraint).

Key Equations

α=τnet/I

angular accelerations are produced by net torques,with inertia opposing acceleration; this is the rotational analog of

a=Fnet/m

τnet=Στi=Iα

the net torque is the vector sum of all the torques acting on the object. When adding torques it is necessary to

subtract CW from CCW torques.

τ=r×F=r⊥F=rF⊥

individual torques are determined by multiplying the force applied by theperpendicularcomponent of the moment

arm

Guidance

In these types of problems it is very important to realize where the application of the force is acting. Remember that

Torque is equal to the Force multiplied by theperpendiculardistance from the rotation axis. So if the CM is the

rotation axis then there is not torque from gravity, as the distance from the rotation axis is zero. Also, in these types

of problems, make sure to use Newton’s laws in the linear form (i.e.ΣF=ma) and also in the rotation form (i.e.

Στi=Iα). Then you can substitute in for one of the unknowns and solve for the other.

Example 1

A wooden disk of mass m and radius r has a string of negligible mass is wrapped around it. If the the disk is

allowed to fall and the string is held so that it unravels without sliding as the disk is falling, what will be the

wooden disk’s acceleration?