Uniform Circular Motion Model: Model Development & Motion

Sections 7.1 & 7.2

What are the assumptions of the uniform circular motion model?

Particle, extended object, 2D circular motion, constant angular velocity

What does uniform circular motion mean?

Uniform= constant

Circular= motion along a circular path

Motion= position is changing

What is angular displacement?

The difference between the final angular position and the initial angular position

What is the symbol and SI unit of angular displacement?

Δ𝜃

Radian (rad)

What is the average angular velocity?

The angular displacement divided by the elapsed time

What is the symbol and SI unit for average angular velocity?

𝜔 (upper bar)

Radian per second (rad/s)

What is instantaneous angular velocity?

The angular velocity at an instant time

What is the symbol and SI unit for instantaneous angular velocity?

𝜔
Radian per second (rad/s)

What is arc length?

The distance traveled along the arc of a circle, equal to the product of the radius and the angle subtended by the arc.

What is the symbol and SI unit for arc length?

s or Δs

meter (m)

What is tangential speed?

The linear speed of a point or particle moving along a circular path, which is equivalent to the magnitude of the tangential velocity

What is the symbol and SI unit for tangential speed?

v_t

meter per second (m/s)

What are the common units for measuring angular displacement?

Revolution

Degree

Radian

What is the conversion factor for 1 rev?

360 degrees

2pi rad

What is the conversion factor for 360 degrees?

2 pi rad

What is the same for the symbol for angular velocity?

𝝎, omega

What is the period for uniform circular motion?

If angular speed is given in revolutions per minute or revolutions per second, then we find the period by taking the reciprocal

When the object is speeding up, the acceleration is in the _______ as the velocity.

Same direction

When the object is slowing down, the acceleration is in the _____ direction of the velocity.

Opposite direction

When the object is changing direction, the acceleration is ______ to the velocity.

Perpendicular

What is the centripetal acceleration?

It is not a new type of acceleration; it describes its direction. It is directed toward the center of the circle.