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Module - Circular Motion & Gravitational Fields G484 - THE NEWTONIAN WORLD Module - Circular Motion & Gravitational Fields Angular Speed LO: Be able to define the radian Be able to convert angles from degrees into radians and vice versa Understand the term angular speed Be able to select and apply the equation for linear speed for bodies undergoing circular motion

Grab a set of compasses, protractor and piece of string… 1) Draw a circle 2) Cut your piece of string so that it equals the radius of the circle 3) Use your piece of string to allow you to draw a segment of arc length = radius 4) How many segments of arc length = radius can be fitted into the whole circle?

One radian is the angle subtended at the centre of a circle by an arc of length equal to the radius.

Convert the following from degrees into radians: 30˚, 90˚, 105˚ Convert the following from radians into degrees: 0.5 rad, 0.75 rad, π rad Express the following as multiples of π radians: 60˚, 180˚, 270˚ o.52 rad 1.57 rad 1.83 rad 28.6o 43.0o 180o 3π/2 π/3 π

θ = c / r Angular Displacement When using radians…  r c The angle of the arc through which the object has moved from its starting position When using radians… θ = c / r  r c

Imagine the object travels through one complete revolution What will its angular displacement be? θ = 2πr / r θ = 2π radians

ω= θ / t Angular Speed What is the angular speed of: We can define the angular speed to be: ω= θ / t It is measured in rad s-1 What is the angular speed of: a) the second hand of a clock? b) the minute hand of a clock? c) the hour hand of a clock?

Period, T The time taken for an object in circular motion to complete one revolution. It is measured in seconds.

Passengers on a fairground roundabout are about 4 Passengers on a fairground roundabout are about 4.0 m from its rotation axis. It rotates once every 12 s. a) Write down the angular displacement in degrees and radians of a passenger after 2s, 6s, 9s and 12s. b) The ticket collector walks radially towards a passenger from the centre of the roundabout at 1.5 ms-1. Through what angle has the roundabout turned when she reaches the passenger?

Objects in circular motion have constantly changing direction. Therefore they have constantly changing velocity. BUT - they can be travelling at a constant speed given by: v = 2πr / T

Homework – Due Friday 14th June Radians and Angular Speed Moving in Circles Calculations