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Basic Circular Motion

100

Define uniform circular motion

What is the motion in a circular path at a constant speed, with continuously changing velocity direction?

200

Name two key characteristics of uniform circular motion

1. Constant speed: The magnitude of velocity (speed) remains the same throughout the motion.
2. Changing direction: The velocity vector changes continuously due to the change in direction along the circular path, causing the object to experience centripetal acceleration.

300

Why is velocity changing in uniform circular motion?

Although the speed is constant, velocity is a vector quantity, meaning it has both magnitude and direction. In uniform circular motion, the direction of the object’s velocity constantly changes as it moves around the circle. Since a change in direction constitutes a change in velocity, even with a constant speed, the object undergoes acceleration.

400

What is the direction of centripetal acceleration

Centripetal acceleration always points towards the center of the circular path. This inward direction ensures the object stays on the circular trajectory instead of moving off in a straight line due to inertia.

500

Explain how speed affects centripetal acceleration

speed increases, centripetal acceleration increases quadratically. For example, doubling the speed results in four times the centripetal acceleration. Similarly, higher speeds require a greater centripetal force to maintain the circular path.

Real World Applicaitons

100

Describe centripetal force in car turns.

When a car takes a turn, it follows a circular path. The frictional force between the tires and the road acts as the centripetal force, keeping the car on the curved path. If friction is insufficient (e.g., on a wet road), the car may slide outward due to inertia.

200

What force keeps satellites in orbit?

The gravitational force between the Earth and the satellite provides the necessary centripetal force that keeps the satellite in its orbit. This force pulls the satellite towards the center of the Earth, preventing it from flying off in a straight line.  

300

Ferris wheel speed: r = 10 m, T = 30 s.

speed is approximately 2.09 m/s. 

v= 2πr/T

400

Calculate orbital speed: T = 5400 s, r = 7000 km.

orbital speed is approximately 8156.48 m/s.

500

If radius increases, how does centripetal force change?

If the radius increases, the centripetal force decreases since force is inversely proportional to the radius. This means that with a larger radius, the same object requires less force to maintain the same speed along the circular path.

Conceptual understanding

100

How does increasing radius affect a_c?

centripetal acceleration is inversely proportional to the radius. As the radius increases (while keeping speed constant), the centripetal acceleration decreases. Thus, for a constant speed, a larger radius requires less centripetal acceleration to maintain circular motion.

200

How does friction act in circular paths?

• Friction provides the centripetal force needed to keep an object moving in a circle. For instance, when a car turns, the frictional force between the tires and the road allows the car to change direction without skidding outwards.
• If the frictional force is insufficient (e.g., on a slippery surface), the object may not maintain its circular path and could slide outward due to inertia.

300

Why does velocity change direction?

In uniform circular motion, the object moves along a circular path, meaning its direction is continuously changing. Since velocity is a vector quantity (having both magnitude and direction), a change in direction results in a change in velocity, even if the speed remains constant. The inward centripetal force causes this continual change in direction, which keeps the object moving in a circular trajectory instead of traveling in a straight line.

400

Compare uniform and non-uniform circular motion.

• Uniform Circular Motion:

  • The object moves in a circular path at a constant speed.
  • The magnitude of velocity remains constant, but the direction changes continuously.
  • Centripetal acceleration is constant in both magnitude and direction.

• Non-Uniform Circular Motion:

  • The object moves in a circular path but at a varying speed.
  • Both the magnitude and direction of velocity change.
  • The centripetal acceleration is not constant; it can vary depending on the speed at different points along the path.

500

Explain why satellites don't fall to Earth.

Satellites remain in orbit due to the balance between gravitational force and their forward motion:

• Gravitational Force: The Earth exerts a gravitational pull on the satellite, providing the necessary centripetal force to keep it in orbit.
• Forward Motion: As the satellite moves forward, it has a tangential velocity that keeps it from falling straight down. Instead of falling directly to Earth, it travels around it in a curved path.
• This balance between the gravitational pull (which acts as the centripetal force) and the satellite's forward inertia creates a stable orbit, preventing it from crashing into the Earth or flying off into space.