- #1

ac7597

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- Homework Statement
- Joe has a simple yoyo, which consists of two disks, each of mass M=0.098 kg and radius R=0.144 meters, connected by a cylindrical spindle of mass m=0.016 kg and radius r=0.01 meters. Joe wraps some string around the spindle; it is made of rough fiber, so it will not slip as it winds and unwinds.

Joe places the yoyo horizontally on a workbench, as shown. He inserts a pin into a tiny hole in center of the bottom disk, so that the entire yoyo is free to rotate without friction around the pin.

What is the moment of inertia of the yoyo around the pin?

Fred now pulls on the string with a constant force T=5.2 Newtons. As he pulls, the string unwinds from the spindle and the yoyo starts to spin.

What is the torque exerted by the string around the pin?

What is the angular acceleration of the yoyo?

How long will it take Fred to pull the string a distance L=0.65 meters?

- Relevant Equations
- torque=|r|*|F|*sin(theta)= I * angular acceleration

total moment of inertia= (1/2) (0.098kg) ( 0.144m)^2 + (1/2) (0.098kg) ( 0.144m)^2 + (1/2) (0.016kg) (0.01m)^2

total moment of inertia= 2.03*10^(-3) kgm^2

torque= 5.2N * (0.144m) = 0.75N*m

thus: 0.75N*m= 2.03*10^(-3) kgm^2 * angular acceleration

angular acceleration = 368.8 rad/s^2

Is the work correct so far?

total moment of inertia= 2.03*10^(-3) kgm^2

torque= 5.2N * (0.144m) = 0.75N*m

thus: 0.75N*m= 2.03*10^(-3) kgm^2 * angular acceleration

angular acceleration = 368.8 rad/s^2

Is the work correct so far?