Rotational Kinematics-Bead Constrained in a Hoop Rotating

In summary, the conversation discusses finding the value of theta in the given equation and determining if the reasoning and answer are correct. It is concluded that the second equation in the attempt at a solution is dimensionally inconsistent and needs to be corrected to theta=arcos(-g/(Rw^2)).
  • #1
Darkalyan
34
0

Homework Statement


http://docs.google.com/Doc?id=d277r7r_58d3chgqfj


Homework Equations


a=w^2*r


The Attempt at a Solution



a=w^2*r
w^2*r*cos(theta)=-mg

theta=arcos(-mg/(Rw^2))

I'm pretty sure that's right, because the vertical component of the acceleration has to equal the vertical component due to gravity. However, I wasn't sure if acceleration was simply w^2*R or if I had to do something more complicated to find it. Is my reasoning/answer correct?
 
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  • #2
That's pretty close. You can see it's not quite right, though, because your second equation in your attempt at a solution part is dimensionally inconsistant. You have a force equal to an acceleration.
 
  • #3
oooh. didn't catch that. thank you. so then i just add a m to the left side of the equation, which makes the m's cancel out, and the final answer is theta=arcos(-g/(Rw^2)) Is that right now?
 

1. What is rotational kinematics?

Rotational kinematics is the study of the motion of objects that rotate around a fixed axis. It involves analyzing the position, velocity, and acceleration of the rotating object at different points in time.

2. What is a bead constrained in a hoop rotating?

A bead constrained in a hoop rotating refers to a scenario where a small object, such as a bead, is moving along the circumference of a larger object, such as a hoop, which is rotating around a fixed axis.

3. How is the motion of a bead constrained in a hoop rotating described?

The motion of a bead constrained in a hoop rotating is described using angular displacement, angular velocity, and angular acceleration. Angular displacement is the change in angle of the bead's position on the hoop, angular velocity is the rate of change of angular displacement, and angular acceleration is the rate of change of angular velocity.

4. What is the role of centripetal force in rotational kinematics?

Centripetal force is the force that keeps an object moving in a circular path. In the case of a bead constrained in a hoop rotating, the centripetal force is provided by the tension in the hoop, which keeps the bead moving along the circumference of the hoop.

5. How do you calculate the centripetal force in rotational kinematics?

The centripetal force can be calculated using the formula F = mv^2/r, where F is the centripetal force, m is the mass of the object, v is the tangential velocity of the object, and r is the radius of the circular path. In the case of a bead constrained in a hoop rotating, the formula can be modified to F = mrω^2, where ω is the angular velocity of the hoop.

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