Solve for Constant Torque: 75g-cm2 to Spin Yo-Yo to 300 rev/min in 1s

In summary, the question asks for the constant torque needed to make a yo-yo spin to 300 rev/min in one second, starting from rest. Using the equation ∑ = Iα and assuming constant angular acceleration, the torque can be found by multiplying the angular acceleration by the moment of inertia. The resulting answer is 2.36 x 10^-4 kg*m^2/s^2.
  • #1
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Homework Statement


A yo-yo has a moment of inertia of 75.0 g-cm2 about its rotation axis. What is the constant torque required to make it spin to 300 rev/min in one second, starting from rest?

Homework Equations


∑
81a69207104f00baaabd6f84cafd15a0.png
= Iα

The Attempt at a Solution


I was thinking since the question is asking for constant torque, angular acceleration would also have to be constant. Therefore, I would just find angular acceleration (using (ω(t) - ω0)/(t2-t1)) then multiply that angular acceleration by the moment of inertia. Is that correct thinking?
 
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  • #2
Yes, your thinking is correct. Be careful with the units.
 
  • #3
What did you get as your answer for this?
 
  • #4
cat__lover said:
What did you get as your answer for this?
2.36 x 10^-4 kg*m^2/s^2
 

1. What is constant torque and how does it relate to spinning a yo-yo?

Constant torque is the amount of rotational force applied to an object over a certain distance. In this case, it is the force needed to spin a yo-yo. It is important because it determines the speed at which the yo-yo will spin.

2. How is torque measured and what unit is used?

Torque is measured in newton-meters (Nm) or in this case, gram-centimeters (g-cm). It is calculated by multiplying the force applied (in newtons or grams) by the distance from the pivot point (in meters or centimeters).

3. What is the significance of the given values, 75g-cm2 and 300 rev/min?

The value of 75g-cm2 represents the constant torque needed to spin the yo-yo to achieve a speed of 300 revolutions per minute (rev/min) in 1 second. This means that the yo-yo will make 300 complete rotations in 1 minute.

4. How does the weight of the yo-yo affect the constant torque needed to spin it?

The weight of the yo-yo does not directly affect the constant torque needed to spin it. However, a heavier yo-yo may require a slightly higher torque due to increased inertia and friction.

5. What factors can affect the ability to achieve a constant torque of 75g-cm2?

The factors that can affect the ability to achieve a constant torque of 75g-cm2 include the quality of the yo-yo's bearings, the smoothness of the string, and any external forces such as air resistance or friction from the surface it is spinning on.

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