Angular Acceleration Homework: Find w/ Radius, Mass

In summary, a string is wrapped around a small hoop with a radius of 0.08m and a mass of 0.18kg. The angular acceleration of the hoop as the string unwinds can be found by using the equation τ = Iα, where τ is torque, I is moment of inertia, and α is angular acceleration. This can be determined by finding the torque using the equation τ = Fd, where d is the perpendicular distance, and then using the moment of inertia of the body.
  • #1
moondawg
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0

Homework Statement


A string is wrapped several times around the rim of a small hoop with radius .08m and mass .18kg. The free end of the string is pulled upward in just the right way so that the hoop doesn't move vertically as the string unwinds. Find the angular acceleration of the hoop as the string unwinds.


Homework Equations





The Attempt at a Solution


So at first i thought i would use 2 equations of torque to find the ang accel(I[tex]\alpha[/tex]=Fd) but that didnt give me the correct answer in the back of the book of 123 rad/sec2. So my friend helped me out and said to set radius x mass equal to MR2[tex]\alpha[/tex]. and that did give me the correct answer i just don't see the logic in setting those 2 equal to each other bc why would r x m be on one side of the equation?! Pleassseee help!
 
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  • #2
Find torque

τ = Fd
d is perpendicular distance

and hope you can find moment of inertia of the body

...

then use

τ = Iα
 

1. What is angular acceleration?

Angular acceleration is the rate at which an object's angular velocity changes over time. It is a measure of how quickly an object is rotating and in what direction.

2. How is angular acceleration different from linear acceleration?

Angular acceleration is a measure of how quickly an object's angular velocity changes, while linear acceleration is a measure of how quickly an object's linear velocity changes. Angular acceleration is measured in radians per second squared, while linear acceleration is measured in meters per second squared.

3. How do I calculate angular acceleration?

Angular acceleration can be calculated by dividing the change in angular velocity by the change in time. The formula for angular acceleration is α = (ω₂ - ω₁) / (t₂ - t₁), where α is angular acceleration, ω is angular velocity, and t is time.

4. How does the radius and mass affect angular acceleration?

The radius and mass of an object do not directly affect angular acceleration, but they do affect the moment of inertia, which is a measure of an object's resistance to changes in its rotational motion. Objects with larger moments of inertia will have smaller angular accelerations for the same amount of torque applied.

5. Can you provide an example of calculating angular acceleration with radius and mass?

Yes, for example, if a solid sphere with a mass of 2 kg and a radius of 0.5 meters is rolling down a ramp with a constant angular acceleration of 4 radians per second squared, the torque can be calculated using the formula τ = Iα, where τ is torque, I is moment of inertia, and α is angular acceleration. The moment of inertia for a solid sphere is (2/5)mr², so τ = (2/5)(2)(0.5)²(4) = 0.8 Nm.

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