5.2 Circular Motion

Question 1

what is one radian defined as?

Answer 1

one radian is defined as the angle subtended at the centre of a circle when the arc length is equal in length to the radius of the circle

Question 2

what is 2π radians equal to?

Answer 2

360° (a full circle)

Question 3

define frequency

Answer 3

no. of complete revolutions per second

Question 4

define period

Answer 4

the time period is the time taken in seconds for one complete circular path

Question 5

what is angular velocity ω?

Answer 5

the rate of angular rotation measured in radians per second, rad s^-1

Question 6

what is the angular velocity formula? (ω)

Answer 6

ω = 2π / T or ω = 2πf

Question 7

what is the formula for constant linear speed in a circle?

Answer 7

v = ωr

Question 8

how do you get to the constant linear speed in a circle equation?

Answer 8

V = d / t
V = 2πr / t
subbing in ω = 2π / T gives you…
v = ωr

Question 9

are objects travelling in circles accelerating?

Answer 9

yes since their velocity is changing because their direction is changing (actual speed in a circle is constant) and acceleration is defined as the rate of change of velocity

Question 10

what is centripetal acceleration?

Answer 10

the acceleration of an object moving in a circle and it is always defined directed towards the centre of the circle

Question 11

what is a key point about circular motion in terms of acceleration and velocity?

Answer 11

there is no acceleration parallel to the direction of motion, velocity remains perpendicular to the direction of the force/acceleration

Question 12

what is the formula for centripetal acceleration?

Answer 12

a = v^2 / r
a = ω^2 x r (since v = ωr)
where a = centripetal acceleration
v = linear velocity
ω = angular velocity
r = radius

Question 13

what is the name of the force that keeps something moving in a circle?

Answer 13

centripetal force

Question 14

what is the definition of centripetal force?

Answer 14

the centripetal force is the resultant force on an object acting towards the centre of the circle, causing it to move in a circular path

Question 15

in what direction does the centripetal force and acceleration act?

Answer 15

radially inwards towards the centre of the circle

Question 16

what is the formula for centripetal force?

Answer 16

F = mv^2 / r
or F = mω^2r
where m = mass
v = velocity
r = radius of the circle

Question 17

why does the speed or KE of the object in circular motion stay constant?

Answer 17

although the force changes the direction of motion, the object’s velocity remains perpendicular to the direction of the force, the object never moves towards or away from the circle, so there is no motion in the direction of the force, hence no work is done on the object, and the object’s KE (and therefore speed) remains constant

Question 18

what is the type of centripetal force acting when a car is travelling around a roundabout?

Answer 18

frictional force

Question 19

what is the type of centripetal force acting when a satellite is orbiting Earth?

Answer 19

gravitational force

Question 20

what is the type of centripetal force acting when a electron orbits the nucleus of an atom?

Answer 20

electromagnetic force

Question 21

what is the type of centripetal force acting when a rubber bung is being spun around on a string?

Answer 21

force of tension

Question 22

in a conical pendulum is the ball in equilibrium?

Answer 22

the ball is in equilibrium vertically but there is a resultant force on the ball directed horizontally towards the centre of the circle (the horizontal component must accelerate the ball towards the centre of the circle)
vertical component of tension T = weight of the ball

Question 23

what is the equation linked to the conical pendulum?

Answer 23

tanθ = v^2 / Rg
where θ = angle from the normal
v = velocity
R = radius of the circle
g = acceleration due to gravity

Question 24

outline an experiment to investigate circular motion using a whirling bung

Answer 24

• tie one end of the thread to rubber bung and make a mark on the string at a distance of 0.3m from the bung
• attach a 1.0N weight at the other end of the string and whirl the rubber bung in a horizontal circle (wear eye protection)
• adjust the speed of rotation such that the radius r of the circle is constant and equal to 0.3m and then continue to whirl the bung at a constant speed
• measure the time, t, for 10 revolutions of the bung
• determine the speed, v, of the bung using s = d / t since the bung is making 10 revolutions, and the circumference is 2πr, then v = 10 x 2πR / T which simplifies to v = 20πr / t
• repeat the experiment for different values of centripetal force F by adding masses to the bottom, an adjusting the speed of rotation till the bung whirls in a circle of the same radius as before, record your results in a table
• plot a graph of force F against v^2, draw a straight LOBF
• the gradient of the line will be equal to m / r
• determine the mass of the bung from the gradient and the value of r used in the investigation (compare with actual mass of bung for validity)

Question 25

when you’ve got roller-coaster carriage spinning on a loop-the-loop roller-coaster where does the passenger feel weightless and why?

Answer 25

they feel weightless at the top because the reaction force on them becomes small, because now their weight provides some of the centripetal force inwards the reaction force is smaller
(reaction force is largest at the bottom)