Module 5 Circular Motion

Question 1

What is constant during uniform circular motion?

Answer 1

speed

magnitude of centripetal force

magnitude of acceleration

Question 2

What changes during circular motion?

Answer 2

velocity

(direction changes, magnitude constant)

Question 3

For circular motion, what is a time period?

Answer 3

time taken for one complete orbit

Question 4

What is the simple formula for speed during circular motion?

Answer 4

speed is 2πr/T

where r is radius of circle and T is time period

Question 5

What is angular velocity or angular frequency (omega)?

Answer 5

is the rate of change of angle

Question 6

What is a radian?

Answer 6

the angle where the arc length is equal to the radius of a circle

Question 7

Why can we say an object in circular motion has an acceleration?

Answer 7

acceleration is the rate of change of velocity

Velocity is a vector and is always changing direction

Meaning v is changing thus mass is accelerating

Question 8

For an object in circular motion, which direction is the acceleration in and thus the resultant or centripetal force?

Answer 8

towards the centre

Question 9

Definition for centripetal force

Answer 9

the resultant force at 90° to the velocity towards the centre of the circle

Question 10

Explain why speed, and therefore kinetic energy are constant for a mass in circular motion?

Answer 10

centripetal force is at 90° to the direction of velocity

No displacement in direction of the force

No work done so mass has constant KE and therefore speed

Question 11

Give examples of three sources of centripetal forces

Answer 11

Gravitational force
Tension
Friction
Normal contact force

Usually vector sum of more than one component of force towards the centre of the circle

Question 12

For an object travelling in a vertical circle, why does the weight have no effect on the value of normal contact force providing the object is at the sides?

Answer 12

weight and normal contact force are at 90° therefore motion is independent

Question 13

For a mass in vertical circular motion, how do you find the tension at the bottom and the top

Answer 13

Find resultant force where RF=mv^2/r

At the bottom, tension>weight so RF=T-W

At the top, tension and weight both act towards the centre of the circle so RF=T+W

Question 14

What In terms of vertical circular motion, what does weightlessness mean?

Answer 14

where the only force creating the centripetal force is weight

Question 15

How to find the speed at which weightlessness will be observed

Answer 15

At top RF=W

W=mv^2/r

W=mg

mg=mv^2/r

Cancel the masses
v^2=rg

Question 16

What is a conical pendulum?

Answer 16

where a mass hanging off a string undergoes circular motion in a horizontal circle with the string at an angle to the vertical

Question 17

Show that the angle to the vertical is independent of the mass for a mass in conical pendulum

Answer 17

For it to be in a horizontal circle vertical RF=0

Fcosø=mg (equal magnitude but opposite direction)

Resultant force in the horizontal is the centripetal force
Fsinø=mv^2/r

Combine the two equations (sin/cos=tan)
tanø=v^2/rg

Question 18

What are the conditions necessary for horizontal circular motion?

Answer 18

resultant forces vertically must = 0 N

resultant horizontal force = centripetal force