Angular speed at bottom of loop

In summary, a circular ring with a mass of 11 kg and radius of 0.66 meters is rolling without slipping about a frictionless vertical loop of radius 10 meters. To barely make it around the top of the loop, the ring must have an angular speed of 25.99 rads/sec at the bottom of the loop. This can be determined using conservation of energy and the rolling equation relating speed of center of mass to angular velocity.
  • #1
Paulie71199
4
0

Homework Statement


A circular ring with a mass of 11 kg and radius of 0.66 meters is to roll without slipping about a vertical loop of radius 10 meters which is frictionless. If it is to just barely make it around the top of the loop, what must its angular speed be at the bottom of the loop in rad/s?


Homework Equations



The moment of inertia for the ring about it's center is I = M R2.

The Attempt at a Solution



The answer comes to be 25.99 rads/sec. Although I don't know how to get to that answer
 
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  • #2
Welcome to PF!

Hi Paulie! Welcome to PF! :smile:

(have a theta: θ and try using the X2 icon just above the Reply box :wink:)

Use conservation of energy (together with the rolling equation relating speed of centre of mass to angular velocity, and putting hte normal reaction force equal to zero at the top). :smile:
 
  • #3
Thank you for the welcome and the help!

Thanks for the tip lol.
 

What is angular speed at the bottom of a loop?

The angular speed at the bottom of a loop refers to the rate at which an object is rotating around a fixed point at the bottom of a circular loop. It is measured in radians per second.

How is the angular speed at the bottom of a loop calculated?

The angular speed at the bottom of a loop can be calculated by dividing the linear speed at the bottom of the loop by the radius of the loop. This can also be calculated using the formula ω = v/r, where ω is the angular speed, v is the linear speed, and r is the radius of the loop.

What factors affect the angular speed at the bottom of a loop?

The angular speed at the bottom of a loop is affected by the radius of the loop, the linear speed of the object, and the gravitational force acting on the object. The shape and incline of the loop can also impact the angular speed.

Why does the angular speed increase at the bottom of a loop?

The angular speed increases at the bottom of a loop because the object is moving faster due to the constant acceleration from gravity. As the object moves down the loop, it gains kinetic energy and its linear speed increases, resulting in an increase in angular speed.

What happens to the angular speed at the bottom of a loop if the radius is decreased?

If the radius of the loop is decreased, the angular speed at the bottom of the loop will increase. This is because a smaller radius means the object has to travel a shorter distance in the same amount of time, resulting in a higher linear speed and therefore a higher angular speed.

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