Calculate angular velocities and alpha values?

In summary, the conversation discusses the dynamics of a lightweight bar with two small spheres attached to either end. The bar is initially vertical and can rotate around a horizontal axis passing through point O, which is located at one-third of the bar's length. The conversation also mentions a slight impact that causes the bar to lose balance and rotate around point O without friction. Two questions are posed, one asking for the calculation of the bar's angular velocities when it is vertical at an angle alpha, and the other asking for the calculation of the angle alpha when one of the spheres, m1, separates from the bar due to a force acting on it. The conversation also suggests finding the moment of inertia of the bar and the vertical height through which the spheres
  • #1
datanhlg
2
0

Homework Statement


A lightweight bar, stiff stick of length L, at either end are two small spheres of mass ##m_{1} = m_{2} = m##. Bar may turn in vertical horizontal axis passing through point O on the way its a bar ##\frac{L}{3}##. At first, the bar is vertical. Due to a slight impact, the loss of balance and start axis through O. Skip any friction.

Homework Equations


a) Calculate angular velocities of the bar when it is vertical with an angle alpha?

b) Know that when the force effects the globe by acting on the ##m_{1}##, with 1,8 times its weight when he began breaking away from the bar. Calculate the alpha angle for the time ball of ##m_{1}## separated from the bar?

The Attempt at a Solution


Please explain for me carefully, thank and sorry my bad English

Here image of this
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  • #2
datanhlg said:
point O on the way its a bar ##\frac{L}{3}##.
Could you please rephrase.
 
  • #3
Assuming by
datanhlg said:
point O on the way its a bar ##\frac{L}{3}##.
you mean its fixed at ##\frac{L}{3}##
First i think you might need to find the moment of inertia of the rod, do that then
find the vertical height through which the ##m_1~and~m_2##fall through and move up respectively. find the total loss in potential energy.
 
Last edited:

Related to Calculate angular velocities and alpha values?

1. How do you calculate angular velocity?

Angular velocity is calculated by dividing the change in angular position by the change in time. The formula for angular velocity is ω = Δθ/Δt. The units for angular velocity are radians per second (rad/s).

2. What is the difference between angular velocity and linear velocity?

Angular velocity refers to the rate of change of angular position, while linear velocity refers to the rate of change of linear position. Angular velocity is measured in radians per second, while linear velocity is measured in meters per second.

3. How do you calculate alpha value?

Alpha value is calculated by dividing the change in angular velocity by the change in time. The formula for alpha value is α = Δω/Δt. The units for alpha value are radians per second squared (rad/s²).

4. What is the relationship between angular velocity and alpha value?

Angular velocity and alpha value are both measures of rotational motion. Angular velocity describes the rate of change of angular position, while alpha value describes the rate of change of angular velocity. They are related by the formula α = dω/dt, where d represents the derivative.

5. Why is it important to calculate angular velocities and alpha values?

Calculating angular velocities and alpha values is important in understanding the rotational motion of objects. It allows us to predict how fast an object will rotate and how quickly its rotation will change. This information is useful in designing and analyzing machinery, vehicles, and other systems that involve rotational motion.

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