# Circular Motion: Write expression for the period in terms of r and g

In summary, circular motion is a type of motion in which an object moves in a circular path around a fixed point. The period of circular motion is calculated using the equation T = 2π√(r/g), where T is the period, r is the radius of the circular path, and g is the acceleration due to gravity. The period is directly proportional to the radius and can be changed by altering the radius or the acceleration due to gravity. A larger value of g will result in a shorter period, while a smaller value of g will result in a longer period.
Homework Statement
1. Draw a free body diagram and solve for the centripetal acceleration in terms of θ and g for one person riding on the amusement park ride in Figure 3. A free-body diagram will show that the centripetal force on the rotating mass m1, is provided by the weight of the hanging mass m2. Since those forces must be equal, we can write the equation: m2g = m1v2/r where v is the velocity of m1, and r is the radius of its circular path. Since the magnitude of the velocity is the average distance divided by the average time, we can write the velocity = the circumference / the period, or v = 2πr/T where the period T is the time to complete one revolution. Assume m2 = 4m1. Write an expression for the period in terms of r and g. You should find the mass terms will drop out.
Relevant Equations
m2=4m1
m2g=m1v2/r
v=2piR
I'm not sure if I'm doing this right as far as coming up with the equation they are asking for. I feel the question is poorly worded and the formatting makes their equation notation difficult to understand. Any insight would be very helpful. This is my work so far:

Without Figure 3, I don't understand why ##m_2g=m_1v^2/r##. Could you please provide the figure?

What leads you to equate tension with centripetal force? Do they have the same magnitude? Do they have the same direction?

On your free body diagram, what body are you focusing on?

## 1. What is circular motion?

Circular motion is the movement of an object along a circular path. This type of motion is characterized by a constant distance from a fixed point, known as the center of the circle, and a constant speed along the path.

## 2. What is the period of circular motion?

The period of circular motion is the time it takes for an object to complete one full revolution along the circular path. It is denoted by the symbol T and is measured in seconds (s).

## 3. How is the period of circular motion related to the radius and acceleration due to gravity?

The expression for the period of circular motion in terms of the radius (r) and acceleration due to gravity (g) is T = 2π√(r/g). This means that as the radius increases, the period also increases, while a larger value of g decreases the period.

## 4. Can the period of circular motion be affected by other factors?

Yes, the period of circular motion can also be affected by the mass and velocity of the object. A higher mass or velocity will result in a longer period, while a lower mass or velocity will result in a shorter period.

## 5. How is the period of circular motion different from the frequency?

The period and frequency are inversely related, with the frequency being the number of revolutions an object completes in one second. The period is the time it takes to complete one revolution, while the frequency is the number of revolutions per second.

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