Motion In A Circle

Question 1

Formula to find arc length

Answer 1

S (m) = r (m) Θ (rad)

Question 2

Defn of angular vel

Answer 2

Angular velocity is the rate of change of its angular displacement over time

Question 3

Formula for angular velocity

Answer 3

ω = dΘ / dt (rad s-1)
= 2π / T
= 2πf

Question 4

Linear/tangential vel formula

Answer 4

V = rω (m/s)

Question 5

Defn of frequency and formula

Answer 5

Frequency of an obj in circular motion is the no. of complete revolutions made per unit time

f = 1/t (s-1 OR Hz - hertz)

Question 6

Defn of period

Answer 6

Period of an object in circular motion is the time taken for it to make one complete revolution

Question 7

Centripetal acceleration defn and formula

Answer 7

Centripetal acceleration is the resultant acc any obj that is moving in a circle experiences

ac = vω = rω^2 = v^2 / r

Question 8

Does the centripetal force do work on obj

Answer 8

No as there’s no displacement of the obj in the direction of the force

Question 9

Where is centripetal acceleration and force directed towards

Answer 9

Centre of the circle

Question 10

Defn of centripetal force and formulas

Answer 10

It is a resultant force that acts towards the centre of the circle

Fc = m ac = mvω = mrω^2 = mv^2 / r

Question 11

What does uniform circular motion mean

Answer 11

The obj is moving in a circle with constant linear speed

Question 12

Why just an obj moving in uniform circular motion experience a force

Answer 12

According to N1L, the obj will continue to move at its constant speed in the same direction unless there is a resultant force acting on it. Hence there must be a force acting on the obj to constantly change its direction of motion

Question 13

Why is centripetal force directed towards the centre of the circle? / why is the force perpendicular to the motion of obj?

Answer 13

Since the obj is moving at constant speed, it does not exp any tangential acc. Hence the direction of its acc and its resultant force must be perpendicular to the direction of motion, which means it will always act towards the centre of the circular motion. Hence the Fc and ac only change its to direction of motion

Question 14

Assuming there is friction
A car is turning on a slope

What changes on rainy days

Answer 14

Check notes on

extension problem solving

Question 15

Vertical circular motion

Where is the string most likely to break and why

Answer 15

Bottom
At top: Fc = mg + T = (m Vtop^2) / r
T = m Vtop^2 / r - mg

At bottom:
T = mg + mVbottom^2 / r

Question 16

Where is the ball most likely to drop when going round a loop

Answer 16

At the top of the loop

Tension becomes N and since the presence of N acting on ___ means that it is in constant with the track

At the top:
Fc = mg + N = (m Vtop^2) / r
N = m Vtop^2 / r - mg

At bottom:
N = mg + mVbottom^2 / r

Question 17

Non-uniform motion

What is the min vel at the top n bottom

Answer 17

Top:
N + mg = Fc 
When Fc = mg, N=0 
mv^2 / r = mg 
Vmin = (rg)^0.5 

Bottom: 
Using COE
mg(2r) + 0.5m Vmin^2 = 0.5m Vb^2 
2gr + 0.5 (rg) = 0.5 Vb^2
4rg + rg = Vb^2 
Min Vb = (5rg)^0.5