# Calculating Angular and Radial Acceleration in Circular Motion

• SUchica10
In summary, circular motion is a type of motion where an object moves along a circular path at a constant speed, while its velocity constantly changes direction. The factors that affect circular motion include the object's mass, the radius of the circular path, and the force acting on the object. Centripetal force, which is calculated by the formula Fc = mv^2/r, is necessary to keep an object in circular motion by constantly changing the direction of its velocity. An object in circular motion can have a constant speed and changing velocity because velocity takes into account both speed and direction.
SUchica10
What are (a) the angular speed, (b) the radial acceleration, and (c) the tangential acceleration of a spaceship negotiating a circular turn of radius 3220 km at a constant speed of 28,700 km/h?

I am not sure what formulas to use... any suggestions would be appreciated.

Last edited:
This is straightforward, check your textbook.

(a) The angular speed, or angular velocity, of the spaceship can be calculated using the formula ω = v/r, where v is the linear speed and r is the radius of the circular turn. In this case, the angular speed would be ω = (28,700 km/h) / (3220 km) = 8.92 radians/hour.

(b) The radial acceleration, or centripetal acceleration, of the spaceship can be calculated using the formula a = v^2/r, where v is the linear speed and r is the radius of the circular turn. In this case, the radial acceleration would be a = (28,700 km/h)^2 / (3220 km) = 256,085.7 km/h^2.

(c) The tangential acceleration of the spaceship can be calculated using the formula a = ω^2r, where ω is the angular speed and r is the radius of the circular turn. In this case, the tangential acceleration would be a = (8.92 radians/hour)^2 (3220 km) = 102,543.2 km/h^2.

## 1. What is circular motion?

Circular motion is a type of motion where an object moves along a circular path at a constant speed. The direction of the object's velocity is constantly changing, but its speed remains the same.

## 2. What are the factors that affect circular motion?

The factors that affect circular motion include the object's mass, the radius of the circular path, and the force acting on the object. These factors can affect the object's speed, direction, and centripetal force.

## 3. How do you calculate centripetal force in circular motion?

Centripetal force is calculated by multiplying the mass of the object by the square of its velocity, and then dividing by the radius of the circular path. The formula for centripetal force is Fc = mv^2/r.

## 4. Can an object in circular motion have a constant speed and changing velocity?

Yes, an object in circular motion can have a constant speed and changing velocity. This is because velocity takes into account the direction of motion, and in circular motion, the direction is constantly changing while the speed remains the same.

## 5. How does centripetal force keep an object in circular motion?

Centripetal force acts as a center-seeking force that pulls an object towards the center of the circular path. This force is necessary to constantly change the direction of the object's velocity, keeping it in circular motion.

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