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.
