Circular Motion

Question 1

Radians

Answer 1

• 1 Radian = The angle at the centre of a circle when the arc length is equal to the radius
• radius*theta = arc length
• 2 pi radians = 360 degrees

Question 2

Converting angles to radians

Answer 2

• Radians to degrees = …x 180/pi
• Degrees to radians = …x pi/180
• when theta is small, tan(theta) = sin(theta)

Question 3

Angular Velocity

Answer 3

• Omega (curly w) = radians per second (rads^-1) = angular velocity
• angular velocity = 2*pi/time period
• angular displacement = change in radians
• Velocity = 2piradius/time period = angular velocity*radius
• Time period = 2*pi/angular velocity

Question 4

Frequency

Answer 4

• Freq. = 1/Time period = no. rotations/time period = angular velocity/2*pi

Question 5

Impulse

Answer 5

• Newton’s second law of motion
• Force * change in time = change in momentum
• linear momentum is always conserved
• increasing the time a change in momentum occurs for will proportionally reduce the force of experienced

Question 6

Kinetic energy and momentum

Answer 6

• kinetic energy (Ek) is 1/2mv^2, momentum (p) is m*v
• p^2 = m^2*v^2, and v^2 = 2Ek/m
• p^2 = m^2* 2Ek/m, so p=sqrt(2mEk) or Ek = p^2/2m
• applies to non-relativstic particles only

Question 7

Elastic and inelastic collisions

Answer 7

• in an elastic collision kinetic energy is not lost, in inelastic collisions some may be
• usually the lost kinetic energy is transferred to internal energy

Question 8

2-dimensional problems

Answer 8

• two equal mass particles have an angle between them of 90 degrees if the collision is elastic
• if a heavier ball strikes a lighter ball at rest the angle is less than 90
• if a lighter ball strikes a heavier ball at rest the angle is greater than 90

Question 9

Centripetal acceleration

Answer 9

• acceleration = velocity^2/radius = radius * angular velocity^2
• centripetal force = mass* centripetal acceleration