Motion in a Circle Flashcards
How does a perpendicular force affect an object?
A perpendicular force changes the body’s direction of motion.
Definition of the angle of a sector
The angle of a sector is the ratio of arc length and the radius of the circle.
Formula for arc sector
s = rθ, 2π rad
s is arc length, r is radius
Definition of the radian
One radian is the angle subtended at the centre of the circle when the arc length is the same as the radius of the arc.
Definition of angular displacement θ
Angular displacement θ is defined as the angle swept by an object moving along an arc about an axis from its angular position to its final angular position. (2π rad)
Definition of angular velocity ω
Angular velocity ω of an object is defined as the rate of change of angular displacement.
What is to note about the linear velocity in a circular path?
The direction of instantaneous linear velocity of a body which is moving in a circular path is always tangential to the circular path at that point.
SI unit for angular displacement and angular velocity
Angular displacement: radians
Angular velocity : rad s^-1
Formula for angular velocity ω
ω = dθ/dt
What is the magnitude of linear velocity(circular path)?
v = ds/dt
v = d(rθ) /dt
v = r dθ/dt
v = rω
What is the definition of period in a circular motion?
Period T in a circular motion is defined as the time taken to complete one revolution.
Formula for period T(circular path)?
T = 2π /ω
Definition of frequency(circular motion)
The frequency f of a circular motion is teh number of revolutions the object makes per unit time.
Formula for frequency(circular path)
SI unit and base unit
f = ω/ 2π
Hertz(Hz), s^-1
At constant angular velocity, what happens to the kinetic energy and the linear momentum?
The kinetic energy is constant but the linear momentum varies.
Definition of centripetal force
Centripetal force is the resultant/net force acting on an object moving in an uniform circular motion.
What is the centripetal acceleration in a circular path?
The acceleration that is perpendicular to the direction of motion because there is no acceleration along the direction of motion(Ke is the same)
In uniform circular motion, what happens to linear velocity, angular velocity and centripetal acceleration?
Linear velocity varies.
Angular velocity is constant.
Centripetal acceleration is varying.
How to find magnitude of centripetal acceleration?(ac)
ac = v^2/r or a = rω^2
How to find magnitude of centripetal force?
F = mac or F = Mrω^2 or F = mv^2/r
For a uniform horizontal circular motion , what happens?
The linear speed and angular speed remains constant.
Centripetal force acts horizontally towards the centre of the circle.
Fy = 0
For a uniform vertical circular motion , what happens?
The linear speed and angular speed remains constant.
Cnetripetal force acts towards the centre of the circle.
For an object to remain in contact, N>0
Fy = Fnet = mv^2/r
For a non-uniform vertical circular motion , what happens?
The magnitude of linear speed changes.
Apply conservation of energy to find speed at any point of motion.
