Finding the Speed of a Point on a Rotating Grinding Wheel

In summary, the conversation discusses finding the speed of a point on a rotating grinding wheel, in which the object initially located on the rim is dislodged and returns to its starting point after one revolution. The equations for the time of the object to rise and fall and the time of one rotation of the wheel are used to determine the speed of the rim. The conversation also includes a request for help in writing the equations and gratitude for the explanation.
  • #1
SsUeSbIaEs
17
0
Can somebody help me with this problem, it is probably pretty easy but I can not seem to think of how to solve it.


A object initially located at point A on the rim of a grinding wheel rotating about a horizontal axis. The object is dislodged from point A when the diameter through A is horizontal. It then rises vertically and returns to A the instant the wheel completes one revolution. Find the speed of a point on the rim if the radius is 1.153 m.
 
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  • #2
We can write an equation for the time of the object to rise and fall as a function of the initial vertical velocity (which is the same as the speed of the rim) and we can write an equation for the time of one rotation of the wheel as a function of the speed of the rim (it actually depends on the speed of the rim and the radius, but the radius is given). If the object is to contact point A when it comes back down, these two times must be equal, so they are the same variable. Now there are 2 equations and 2 variables, so all that's left is to solve the system of equations.

Do you need help writing the equations or is this enough?

cookiemonster
 
  • #3
I need help writing the equations.
 
  • #4
[tex]
\Delta y = \frac{1}{2} a t^2 + v_0 t
[/tex]
We note that [itex] \Delta y = 0 [/itex] and [itex] a = g = -9.8 m/s^2 [/itex], so the only two variables left are t and [itex] v_0 [/itex]. That's one equation.

[tex]
t = \frac{distance}{velocity} = \frac{circumference}{speed} = \frac{2 \pi r}{v_0}
[/tex]
We note that r = 1.153m, so we again have two variables.

This gives us two equations and two variables.

cookiemonster
 
Last edited:
  • #5
THANKYOUTHANKYOU THANKYOU

Thank you so much that makes a lot of sense!
 
  • #6
THANKYOUTHANKYOU THANKYOU

Thank you so much that makes a lot of sense!
 

1. What is the difference between rotation and rigid bodies?

Rotation refers to the circular movement of an object around a fixed point or axis, while rigid bodies are objects that do not change shape or size when subjected to external forces.

2. How is rotational motion measured?

Rotational motion is measured in units of radians or degrees, which represent the angle of rotation. It can also be measured in terms of angular velocity, which is the rate at which an object rotates.

3. What is the moment of inertia?

The moment of inertia is a measure of an object's resistance to rotational motion. It is affected by the object's mass, shape, and distribution of mass around the axis of rotation.

4. How do external forces affect rotational motion?

External forces, such as torque or friction, can cause changes in the rotational motion of an object. Torque can cause an object to rotate, while friction can slow down or stop rotational motion.

5. What is the difference between rotational and translational motion?

Rotational motion refers to the movement of an object around an axis, while translational motion refers to the movement of an object from one position to another. Both types of motion can occur simultaneously in an object.

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