How Accurate Is the Calculation of Angular Acceleration and Time for a Yo-yo?

In summary, the total moment of inertia is 2.03*10^(-3) kgm^2 and the torque is 0.75N*m. The angular acceleration is 368.8 rad/s^2. The correct torque calculation is (1/2) (0.016kg) (0.01m)^2 and the time for a 90 degree rotation is 2.25 seconds. The linear distance is 0.65m and the radians is 65 rad.
  • #1
ac7597
126
6
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?
 

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  • #2
Looks like you have the string wrapped around the edge of a disk.
 
  • #3
Is the torque just involves the cylindrical spindle thus :
torque= (1/2) (0.016kg) (0.01m)^2 ?
 
  • #4
ac7597 said:
Is the torque just involves the cylindrical spindle thus :
torque= (1/2) (0.016kg) (0.01m)^2 ?
Did you mean that? You seem confused between torque and moment of inertia.
 
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  • #5
ac7597 said:
Is the torque just involves the cylindrical spindle thus :
torque= (1/2) (0.016kg) (0.01m)^2 ?
That wasn't what I meant. I meant that you used the wrong lever arm in computing the torque. I think it would help you to see how to do it if you drew a diagram looking at the yoyo along the direction of the pin, showing the string and the outline of the disks and the spindle.
 
  • #6
sorry about the mistake.
total moment of inertia= 2.03*10^(-3) kgm^2

torque= 5.2 * 0.01 = 5.2 E-2
angular acceleration = (5.2 E-2)/ (2.03E-3)= 25.6 rad/s^2

I don't know how to solve for the time.
 
  • #7
ac7597 said:
how to solve for the time.
Through what angle will it have rotated?
 
  • #8
90degrees
 
  • #9
ac7597 said:
90degrees
How do you get that?
 
  • #10
linear distance = radians * radius
0.65m= radians * 0.01m
radians= 65 rad

thus with kinematics:
65rad= (1/2) (25.6) *time^2
time=2.25 seconds
 
  • #11
ac7597 said:
linear distance = radians * radius
0.65m= radians * 0.01m
radians= 65 rad

thus with kinematics:
65rad= (1/2) (25.6) *time^2
time=2.25 seconds
Looks good.
 

Related to How Accurate Is the Calculation of Angular Acceleration and Time for a Yo-yo?

What is torque?

Torque is a measure of the rotational force that is applied to an object. It is calculated by multiplying the applied force by the distance from the axis of rotation to the point where the force is applied.

How is torque related to a yoyo?

In the case of a simple yoyo, torque is created when the user exerts a force on the string, causing the yoyo to spin around its axis of rotation. The distance from the axis of rotation to the point where the force is applied is the length of the string.

What factors affect the torque of a yoyo?

The torque of a yoyo is affected by several factors, including the force applied to the string, the length of the string, the mass of the yoyo, and the shape and size of the yoyo.

How does torque affect the performance of a yoyo?

The amount of torque applied to a yoyo can greatly affect its performance. A higher torque can result in a longer spin time and a faster rotation, while a lower torque may cause the yoyo to slow down or stop spinning altogether.

Can the torque of a yoyo be increased?

Yes, the torque of a yoyo can be increased by increasing the force applied to the string or by increasing the length of the string. Additionally, using a yoyo with a larger mass or a different shape can also increase the torque.

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