Module 5 - Circular Motion (Kinematics of Circular Motion) Flashcards
What is meant by circular motion
object moving in a circular path within a single, flat plane, maintaining a constant distance from a central point.
What is meant by the radian
A precise measure of angle that uses the inherent properties of a circle - its radius- to approximate angles
What is one Radian equal to in degrees
57.3 Degrees
What is one radian equal to in terms of its arc length and radius
One radian is equal to the ratio between a circles circumference and its radius
What is the equation for arc length in radians
s = θr
s - arc length
θ - angle
r - radius
What is the equation of radians in terms of degrees
radians = degrees x π/180
What is the equation for degress in terms of radians
degrees = radians x 180/π
What is meant by angular velocity
The change in angle of a body in circular motion per unit time
What is meant by Time period
The time taken for an object in circular motion to complete one oscillaltion
What is meant by Frequency
The number of oscillations an object in circular motion completes per unit time
Give the base equation for angular velocity
ω = θ/t
ω - angular velocity
θ - angle progression
t - time
Give the equation for angular velcocity for a full oscillation
ω = 2π/T
ω - angular velocity
T - time period
Give the equation for angular velocity including frequency and derive it
ω = 2π/T
T = 1/f
ω = 2πf
Explain ω = 2πf conceptually
ω, is the number of radians per unit time, 2π is the number of radians in one oscillation, f is the number of oscillations per unit time, therefore 2πf, is the total number of radians in the number of oscilaltions per unit time.
What is the unit for angular velocity
rad s⁻¹
What is meant by linear speed
The distance travelled per unit time
Give the equation for linear speed
v = s/t
If two objects in circular motion, about the same point, are in sync but have different radii descirbe fully, their:
- Angular Velocity
- Linear Velocity
Both objects have the same angular velocity as they start and finish their oscillations at the same time. However, they have different linear velocities, the one with the greater circumference and therfore radius will have a greater linear velocity as it must cover a greater distance in the same time to be in sync with the one with the smaller radius
For constant speed in a circular motion what factors affect linear speed
- Radial Length, the greater the radius for the, for a constant speed, the particle must travel a greater distance in the same time, meaning v ∝ r
- Angular Velocity, The greater the angle progression per unit time, the grater the distance through the circle travelled per unit time, meaning v ∝ ω
What is the equation linking angular and linear velocity
v = rω
Derive v = rω
s = θr
DIFFERENTIATE WITH RESPECT TO t:
ds/dt = d/dt (θr)
FACTOR R:
ds/dt = r(dθ/dt)
SUBSTITUTE
ds/dt = v
dθ/dt = ω
v = rω
