# Question on uniform circular motion

• jactre
The formulas provided are correct, but the value for r should be the sum of the radius of Earth (6.38 x 10^6 m) and the height of the satellite (589,000 m). This will give you the correct values for velocity and acceleration.In summary, the Earth satellite in a circular orbit 589 km above the Earth's surface has a period of 96.26 min. The speed of the satellite can be calculated using the equation v= (2pi x r)/T, where T is the period converted into seconds and r is the sum of the radius of Earth and the height of the satellite. Similarly, the magnitude of the centripetal acceleration can be calculated using the equation a= v^2
jactre
An Earth satellite moves in a circular orbit 589 km above Earth's surface with a period of 96.26 min. What are (a) the speed and (b) the magnitude of the centripetal acceleration of the satellite?

I know I need the equations for 1) period and 2) centripetal acceleration and 3) r.

1) T= (2pi x r)/v (seconds)
2) a= v^2/r (m/s^2)
3) 589 km

I converted T=92.26 min into seconds and got 5775.6s and converted 589km to meters. I then plugged these numbers into equation 1 to solve for velocity (v= (2pi x r)/T). I used this velocity as well as 589,000m for r to find acceleration using equation 2.

The answers I calculated for both velocity and acceleration are wrong, and I think my problem lies in my value for r.

Did I interpret this incorrectly? Any input on what r should be (or if I made another mistake) is greatly appreciated! Thank you!

Earth's surface is not its center; "An Earth satellite moves in a circular orbit 589 km above Earth's surface..."

## 1. What is uniform circular motion?

Uniform circular motion is a type of motion in which an object moves along a circular path at a constant speed. This means that the magnitude of the object's velocity remains constant, but its direction is continuously changing.

## 2. How is uniform circular motion different from regular circular motion?

In regular circular motion, the speed of the object may vary as it moves along the circular path. However, in uniform circular motion, the speed remains constant throughout the motion.

## 3. What is the role of centripetal force in uniform circular motion?

Centripetal force is the force that keeps an object moving in a circular path. In uniform circular motion, the centripetal force is responsible for continuously changing the direction of the object's velocity, while the magnitude remains constant.

## 4. How is the centripetal force calculated in uniform circular motion?

The centripetal force can be calculated using the equation F = mv²/r, where F is the force, m is the mass of the object, v is its velocity, and r is the radius of the circular path.

## 5. What are some real-life examples of uniform circular motion?

Some examples of uniform circular motion include the motion of a satellite orbiting around a planet, the rotation of a washing machine drum, and the movement of a carousel at a carnival.

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