Question

A homemade yo-yo has been fashioned from two identical disks connected by a central axle; the axle has a radius much less than that of the disks. A light, thin string is wound several times around the axle. This question is about pulling the yo-yo along the floor, rather than using the yo-yo in the usual way. The coefficient of static friction between the yo-yo and the floor is 0.850, and the coefficient of kinetic friction is 0.780. The mass of the yo-yo is 250.0  grams , and the center of mass of the yo-yo is on the central axis of the axle exactly halfway between the two disks. The radius of the disks is 37.40  mm , the radius of the axle is 7.00  mm , and the rotational inertia of the yo-yo is 0.000200  kg⋅m2 (i.e. 2.00×10⁻⁴  kg⋅m2 ). Three different experiments will be described in which the yo-yo is pulled in a slightly different manner, but always with a pulling force of magnitude 0.0360  N .

find the size of the torque due to the friction force and the size of the torque due to the pulling force (both torques are about the central axis).

Answer 1

Torque due to friction force (about the central axis) = fs (rdisk)

rdisk = 0.0374 m

Torque due to pulling force (about the central axis) = 0.036 raxle = 0.036*0.007 = 0.000252 N-m

Net torque = I*alpha

0.000252-fs(0.0374) = 0.0002 (alpha)

alpha is angular acceleration

F = fs + ma

a = alpha *0.0374

0.036 = fs +0.25(alpha*0.0374)

0.036 = fs +0.25*0.0374*(0.000252-0.0374fs)/0.0002

0.024219 = -0.74845 fs

fs = -0.03235 N

Torque due to friction force = -0.00121 N-m