16 : Circular motion

Question 1

angular velocity

Answer 1

• rate of change of angle
• ω = θ/t
• when a t = one full revolution
• ω = 2π /T
• =2π f
• rads^ -1

Question 2

centripetal force

Answer 2

• always acts towards centre of a circle
• acting perpendicular to velocity
• no work is done on object and as a result speed and kinetic energy is constant

Question 3

linear velocity

Answer 3

• s= d/t
• in one complete rotation
• v= 2πr / T
• and as ω = 2π /T
• linear velocity = rω

Question 4

comparing objects velocity

Answer 4

• same time to complete one rotation
• doubling the radius the line velocity is also doubled
• but all have the same angular velocity

Question 5

centripetal acceleration

Answer 5

• the acceleration of any object travelling in a circular path at a constant speed = centripetal acceleration
• a = v^ 2 /r
• or a = ω^ 2 r
• speed is constant but velocity is constantly changing as its direction changes
• always directed towards the centre of the circle

Question 6

acceleration and force

Answer 6

• objects speed remains constant becasue the component of the frce acting on the object in the direction of motion is zero
• f = mv^ 2/ r
• or F =mω^ 2 r
• acts towards the centre of the circular path

Question 7

Banked surfaces

Answer 7

• the greater the sped of an object on a circular path the greater the centripetal force required to follow this path
• the horizontal component of normal contact force together with frictional force provide the centripetal fore