Determine the angular speed ##\dotθ## of the arm OC

In summary, the problem involves a collar sliding along a spiral-shaped guide rod and a pin on the collar sliding in a slotted arm OC. The goal is to determine the angular speed ##\dot θ## of the arm OC in terms of the constant speed v0, the spiral parameter b, and the angle θ. The given solution is ##(\frac {v_0} {b}) (1+θ^2)^{-1/2}##, and the only other information provided is that ##v_R=\dot R=b \dotθ = v_0## and ##v_θ=R\dotθ##.
  • #1
Alexanddros81
177
4

Homework Statement


13.30 The colar B slides along a guide rod that has the shape of the spiral R = bθ.
A pin on the collar slides in the slotted arm OC. If the speed of the collar is constant at v0,
determine the angular speed ##\dot θ## of the arm OC in terms of v0, b, and θ.

P13_29-P13_30.jpg

Homework Equations

The Attempt at a Solution



The solution given: ##(\frac {v_0} {b}) (1+θ^2)^{-1/2}##

What I have only done is : ##v_R=\dot R=b \dotθ = v_0##
and ##v_θ=R\dotθ##
Any hints?
 
Physics news on Phys.org
  • #2
Alexanddros81 said:

Homework Statement


13.30 The colar B slides along a guide rod that has the shape of the spiral R = bθ.
A pin on the collar slides in the slotted arm OC. If the speed of the collar is constant at v0,
determine the angular speed ##\dot θ## of the arm OC in terms of v0, b, and θ.

View attachment 211424

Homework Equations

The Attempt at a Solution



The solution given: ##(\frac {v_0} {b}) (1+θ^2)^{-1/2}##

What I have only done is : ##v_R=\dot R=b \dotθ = v_0##
and ##v_θ=R\dotθ##
Any hints?
You are told the speed is v0. ##\dot R## is only one component of that.
 
  • #3
Pytels_Dynamics069.jpg


I guess this is correct.
 
  • #4

1. What is angular speed in relation to the arm OC?

Angular speed, represented by the symbol ##\dotθ##, refers to the rate of change of the angular displacement of the arm OC over time. It is a measure of how fast the arm is rotating around point O.

2. How is angular speed calculated for the arm OC?

The angular speed of the arm OC can be calculated by dividing the change in angular displacement (##Δθ##) by the change in time (##Δt##). This can be represented by the formula ##\dotθ = \frac{Δθ}{Δt}##.

3. What is the unit of measurement for angular speed?

Angular speed is typically measured in radians per second (rad/s) or degrees per second (°/s). The choice of unit depends on the unit used for angular displacement (radians or degrees) and the unit of time (seconds).

4. How does angular speed differ from linear speed?

Angular speed refers to the rotational motion of the arm OC, while linear speed refers to the straight-line motion of a point on the arm. Angular speed is measured in radians or degrees per second, while linear speed is measured in meters or feet per second.

5. What factors can affect the angular speed of the arm OC?

The angular speed of the arm OC can be affected by the length of the arm, the radius of rotation, and the force applied to the arm. Additionally, friction, air resistance, and the mass of the arm can also impact the angular speed.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
2
Replies
38
Views
2K
  • Introductory Physics Homework Help
Replies
17
Views
3K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
3K
  • Introductory Physics Homework Help
Replies
5
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
8K
  • Introductory Physics Homework Help
Replies
9
Views
6K
  • Introductory Physics Homework Help
Replies
1
Views
2K
Back
Top