Circular Motion Flashcards
What is the definition of radians?
Radians are a measure of angular displacement, defined as the distance traveled around a circle divided by the radius of that circle.
360 degrees = 2π radians
What is the relationship between period and frequency?
Period is the time to complete one full oscillation, while frequency is the number of complete oscillations per unit time.
Frequency (f) is the reciprocal of the period (T): f = 1/T
What is angular speed?
Angular speed is the rate of change of angular displacement with respect to time, measured in radians per second.
Fill in the blank: The centripetal force is always directed towards the _______.
center of the circle
What is centripetal acceleration?
Centripetal acceleration is the acceleration of an object towards the center of a circle when the object is in motion at constant speed.
What are the properties of an object moving in a circle?
-Period
-Frequency
-Angular displacement
-Angular velocity
What’s the equation for linear velocity?
V=rω
Where V is linear velocity, r is the radius, and ω is angular speed.
What is the formula for centripetal force?
F=mv^2/r or F=mω^2r
Where m is mass, v is linear velocity, ω is angular velocity and r is the radius.
What is the formula for angular displacement in circular motion?
Δθ = ω * Δt
Where Δθ is angular displacement, ω is angular speed, and Δt is the change in time.
Or; Δθ = s/r
Where s is the distance traveled around the circle, (arc length) and r is the radius.
Angular speed equation
Angular speed (ω) can be calculated as ω = Δθ / Δt
Where Δθ is angular displacement and Δt is change in time.
Or: ω=2(pi)/T
What does the Centripetal Force do?
This force is necessary to keep an object moving in a circular path.
Centripetal Acceleration Formula.
Centripetal acceleration (a) can be calculated using the formula a = v²/r
Where v is linear speed and r is the radius.
Or: a=rω
Method to investigate Circular Motion?
1- Tie a bung of mass m horizontally to a string.
2- Thread the string through a glass tube and paper clip vertically and sit a heavier mass of M at the bottom.
3- Swing the bung in a horizontal circle.
4- Record time taken for 10 complete circles and repeat 3 times.
5- Find a time for one oscillation.
Change masses and repeat.
Evaluation of practical to investigate Circular Motion?
- As bung swing, big M is stationary when Mg is equal to centripetal force.
-If the centripetal force > Mg: M moves up.
-If the centripetal force < Mg: M moves down.
-As bung circles, tension changes direction continuously.
-Magnitude of tension changes continuously.
- T is max at bottom of circle and min at top.
-Direction of weight is constant, resultant force varies on position of bung.
-At bottom of circle: T > Mg
TMax = (mv^2)/r + mg.
-At top of circle: T<Mg
TMin = (mv^2)/r - mg
-Acceleration and speed is slowest at top and fastest the bottom of circle.
