Further Mechanics

Question 1

What is a radian ?

Answer 1

When the arc length is the same size as the radius the angle is equal to 1 radian

Question 2

the angle in radians is given by ?

Answer 2

arc length / radius

Question 3

angle in radians =

Answer 3

angle in degrees x 2pi/360

Question 4

angle in degrees =

Answer 4

angle in radians x 360/pi

Question 5

what is angular speed ?

Answer 5

Angular speed is the angle turned through per second. Angular speed = angle turned (rads) / time (s). Units are rads^-1

Question 6

💿 what is the angular speed of 2 points on this CD. Both points are in line with one another, one is on the outer edge and the other is on the edge of the inner circle.

Answer 6

• both points have the exact same angular speed
  -as they will both always take the same amount of time to turn through a full rotation
  -point A will however have a greater linear speed as it has to travel a further distance

Question 7

How to calculate angular speed ?
For a complete revolution, an object turns through 2pi in one time period

Answer 7

Angular speed = 2pi/ T(s)
-f=1/T therefore angular speed= 2pif(Hz/rads^-1)

Question 8

What is the angular speed of a point on the earths surface ?

Answer 8

(24 hours is one whole revolution of earth)
T= 24x60x60= 86400s
Angular speed = 2pi / 86400 = 7.27x10^-5 rads^-1

Question 9

Angular speed equations to memorise

Answer 9

W= angle/time
W= 2pi/ time period
W= linear speed /radius
W=2pif
F=1/T

Question 10

The international space station completes 16 orbits of the earth every day. The radius of the orbit is 6500km. What is its linear speed ?

Answer 10

W=v/r
Angular speed = 2pi/T = 16x2pi / 24x60x60 =1.2X10^-3
MAKE SURE TO USE M NOT KM
V=wr
V= (1.2X10^-3) X (6500 X 10^3 )
V= 7600MS^-1

Question 11

What is centripetal acceleration ?

Answer 11

• as an object travels in a circular path its direction is constantly changing
• therefore its velocity must be constantly changing as velocity is a vector
• this acceleration is known as centripetal acceleration and is directed towards the centre of the circle and perpendicular to the velocity

Question 12

How to calculate centripetal acceleration ?

Answer 12

A= angular speed squared x radius
A = linear speed squared / radius

Question 13

The pods on the outside of the London eye take 30 mins to complete a full rotation. The diameter of the wheel is 100m. What is the centripetal acceleration of one of the pods ?

Answer 13

T= 30X60= 1800s
Angular speed = 2pi/T w= 2pi/1800 = 3.5x10^-3 rads^-1
**Now plug into centripetal acceleration equation **
A=w^2r = (3.5x10^-)^2 x (100/2)= 6.1x 10^-4 ms^-2

Question 14

What is a centripetal force ?

Answer 14

Newton’s first law: an object will continue travelling at a constant speed in a straight line unless acted on by a resultant force
- therefore for an object to follow a circular path a force must at on it
- this is known as a centripetal force.
- just like centripetal acceleration it is directed towards the centre of the circle and perpendicular to the velocity

Question 15

Centripetal force is not a force itself

Answer 15

• the centripetal force is provided by a force acting towards the centre, for example friction, gravity, tension.
  Eg. Car going around a roundabout: centripetal force provided by friction

Question 16

What happens when a ball tied to a rope is moving in a circular path and then the centripetal force is removed (eg. String is cut) ?

Answer 16

• the object will fly off at a tangent
• one the centripetal force is removed, you are back to newtons 1st law