Can a pendulum have a constant speed in vertical circular motion?

[Allandra]

Homework Statement

Can a pendulum that swings in a vertical circle have a constant speed throughout its motion?
How can I explain this phenomenon using angular velocity? Is there any instance when such case happen?

Homework Equations

1/2mv2 = mgh
velocity= radius X angular velocity

The Attempt at a Solution

Nope. When the pendulum swings up some of the kinetic energy is being converted to potential energy and thus the speed of the pendulum decreases. OR
The angular velocity of the pendulum decreases(why?)

 

[kuruman]

You have already established that the linear speed decreases because the kinetic energy decreases. If v decreases and r stays the same, what happens to the angular velocity? Look at your second equation. By the way, kinetic energy has v² in it, not just v.

 

[Allandra]

The velocity decreases because at it comes near the top of the circle, the radius(of the vertical circle)decreases and since angular velocity is constant and depends only on the time it takes for one revolution. Thx! ^_^ Lol sry 4 the equation mistake.

 

[kuruman]

Let's take it from the top.

KE = (1/2)mv²; PE = mgh

The total mechanical energy is constant, KE + PE = Constant

Therefore when the pendulum goes higher, two things happen PE increases because h increases and KE decreases to keep the sum KE + PE constant.

But if KE decreases, v must also decrease.

Now in terms of angular velocity ω, v = ω r.

Here, r is the length of the pendulum. This stays constant as the pendulum swings back and forth.

So ...

Looking at v = ω r, if v decreases and r stays the same, what happens to ω?

 

[Allandra]

Lol ok the angular velocity decreases. Sry because I confuse it w/horizontal circular motion.