Module 5: Chapter 16 - Circular Motion Flashcards
What is the equation for the linear speed of an object in uniform circular motion?
v = 2πr/T
v = 2πrf
r = radius, T = period, f = frequency
What is angular displacement (θ)?
The angle swept out at the centre of a circular path (in radians)
What is the equation for arc length?
when in radians
s = rθ
arc length = radius x θ
What is angular speed (ω)?
The rate of change of angular displacement
What is the equation for angular speed (ω)?
angular speed = angular displacement / time
ω = Δθ/t
ω = 2π/T
t = time, T = period
What are the units for angular speed?
rad s⁻¹
(can also be r.p.m)
What is angular frequency?
Angular frequency is the same as angular speed
What is the equation for angular frequency?
ω = 2πf
Show how angular frequency is the same as angular speed:
Angular speed = Δθ/t
= 2π/T
= 2π 1/T
= 2πf
= Angular frequency
T = time for one full revolution
What is the relationship between angular and linear speed?
v = rω
linear speed = radius x angular speed
Derive the relationship between angular and linear speed?
ω = 2π/T
v = 2πr/T
= r x 2π/T
= rω
What is centripetal acceleration?
The acceleration of any object travelling in a circular path at constant speed, which always acts towards the centre of the circle
What are the 3 equations for centripetal acceleration?
- a = v²/r
- a = rω²
- a = vω
v = linear speed, r = radius, ω = angular speed
What is the radius of the earth?
6400km
What is the height above sea level of the iss’s orbit?
400km
What are the 4 equations for centripetal force?
- F = mv²/r
- F = mrω²
- F = mvω
- F = ma
m =mass, v =linear speed, ω = angular speed, a = centripeal acceleration
What is centripetal force?
The resultant force that keeps a body moving with a constant speed in a circular path
A mass of 300g is whirled around a vertical circle using a piece of string of length 20cm at 3.0 revolutions per second. Calculate the tension in the string at positions:
a) Top
b) Bottom
c) String Horizontal
a) 18.4 N
b) 24.3 N
c) 21.3 N
What is the expression for the centripetal force at each position?
a) CF = T + W
b) CF = T
c) CF = T - W
T = Tension, W = Weight
What happens if centripetal force is removed?
The object will continue along a straight line tangentially to the circular path
The maximum speed of a car (without skidding) of mass 750kg around a roundabout of radius 20m is 9ms⁻¹, calculate the centripetal force at this speed
3038N
A car is racing on a track banked at 25 degrees to the horizontal on a bend with a radius of curvature of 350m. Show that the maximum speed at which the car can take the bend without sideways friction is 40ms⁻¹
VERY IMPORTANT QUESTION
What will happen to a car if it takes a bend at increasing speeds?
The radius of the cars circular motion will increase
Explain how questions involving banked slopes can be calculated:
IMPORTANT
As there is a normal force acting on the object due to the banked slope, it can be resolved into vertical and horizontal components. We assume the vertical component of N balances out the weight, from this you can then calculate N. Once you have calculated N, you can calculate the horizontal component of N which is the centripetal force
The vertical component of N does NOT actually balance out the weight, however this must be used to yield the correct result from the calculations. DO NOT RESOLVE WEIGHT TO FIND N.
Why are you pushed into your seat at the bottom of a roller coaster and “feel heavier”?
At the bottom of the roller coaster “Centripetal Force = Normal Force - Weight”, therefore “Normal Force = Centripetal Force + Weight”. Since Weight and Centripetal Force are constant, you experience a greater force at the bottom of the roller coaster
Why does an object in circular motion remain at a constant speed despite a resultant force acting upon in?
The resultant force is at 90 degrees to the velocity of the object
What does a graph of centripetal force against v² look like?
Positive Linear graph
What is the relationship between linear velocity and the radius (when the angular velocity is constant)?
Directly proportional
