A yo-yo is made from two uniform disks connected by a light axle of radius 0.43

Question

A yo-yo is made from two uniform disks connected by a light axle of radius 0.43 cm. We can model its moment of inertia as a single uniform disk of total mass 48.0 g and radius 1.88 cm, essentially ignoring the contribution of the axle to its moment of inertia. A light, thin string is wound several times around the axle. As a yo-yo master, you've mastered the technique of holding the end of the string and watching the yo-yo slowly unravel as it falls toward the floor. Use conservation of energy to determine how fast the center of mass of the yo-yo is moving after it has fallen a distance 0.9 m while unraveling.

Explanation / Answer

Given: mass of equivalent disc 'm' = 48 g; radius of that disc 'r' = 1.88 cm, distance by which the center of mass of the Yo-Yo falls 'h' = 0.9 m

Therefore the moment of inertia of disc 'I' = 0.5*m*r2  

Now the decrease in potential energy = increase in kinetic energy of the Yo-Yo (energy conservation)

m*g*h = 0.5*I*2  = 0.5*I*v2/r2 {using = v/r}

So m*g*h = 0.5*(0.5*m*r2)*v2/r2

or v = (4*g*h)0.5  = (4*9.8*0.9)0.5  = 5.94 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.