Linear Speed and Circular Motion Problem

In summary: Newton's 3rd law states that for every action, there is an equal and opposite reaction. In summary, the problem involves an air puck rotating in a circular path with a mass suspended in equilibrium. The task is to find the magnitude of the force maintaining the circular motion and the linear speed of the puck. This requires using equations involving the mass, radius, and angular speed. However, additional variables are needed and the use of Newton's 3rd law may be necessary.
  • #1
Cheapo2004
9
0
Ok, I am having a hard time figuring this problem out for two reasons, the first is that my teacher is very tricky, 2nd is that I'm not sure how to work it out.

An air puck is tied to a string and allowed to revolve in a circle with circumference if 2pi. The other end of the string passes through a hole in the center of the surface and a mass of 1kg is tied to it. If the suspended mass remains in equilibrium..
A) What is the magnitude of the force that maintains the circular path
B) What is the linear speed of the puck

So, what I got out of this question is:
2pi*r = cir... so r=1
m = 1kg

So, with the information given, we need to find Fc (force that maintains circular path). The equations i have to find this are:

Fc = m*(vt^2) / r
Fc = m*r*(w^2)
(w meaning angular speed)

So, for either equation i need to find w, or vt. The equations i have for these are:

vt = r*w
w = Delta Theta / Delta T

So by moving from equation to equation I'm still missing 2 variables, I can't figure it out

Any help is appreciated!
 
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  • #2
Use Newton III for A.
 
  • #3
Päällikkö said:
Use Newton III for A.
...? Newton's 3rd law...?
 

FAQ: Linear Speed and Circular Motion Problem

What is linear speed and how is it different from angular speed?

Linear speed is the rate at which an object is moving in a straight line. It is measured in units such as meters per second or kilometers per hour. On the other hand, angular speed is the rate at which an object is rotating around a fixed point. It is measured in units such as radians per second or revolutions per minute.

How do you calculate linear speed?

Linear speed can be calculated by dividing the distance an object travels in a given time by the time it took to travel that distance. The formula for linear speed is: v = d/t, where v is the linear speed, d is the distance, and t is the time.

Can an object have a constant linear speed but varying angular speed?

Yes, an object can have a constant linear speed but varying angular speed. This can happen when the object is moving in a circular path at a constant speed, but the distance from the center of rotation changes. This results in a change in angular speed, but the linear speed remains constant.

How does the radius of a circular path affect the linear speed of an object?

The radius of a circular path has a direct effect on the linear speed of an object. As the radius increases, the linear speed also increases, and vice versa. This is because the greater the distance from the center of rotation, the greater the distance the object needs to travel in a given amount of time, resulting in a higher linear speed.

What is the relationship between linear speed and tangential speed?

Tangential speed is a type of linear speed that is measured at a tangent to the circular path of an object. The two are directly related, as tangential speed is equal to the linear speed multiplied by the cosine of the angle between the linear speed and the radius of the circular path. In other words, tangential speed is a component of linear speed in the direction of the tangent to the circular path.

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