Circular MotionCircular MotionObjectivesObjectives

Students should be able to:Students should be able to:

(a)(a) define the define the radianradian;;

((b)b) convert angles from degrees convert angles from degrees into radians and vice versa; into radians and vice versa;

Outcomes Outcomes • All should• Be able to define the radian.• Be able to convert degrees into radians and vice-versa.• Most Should• Be able to understand the reasons for using radians.• Be able to solve problems involving a mixture of degrees

and radians.• Some Could• Be able to explain what the idea of centrifugal force is and

why it is imaginary.• Be able to derive the equations for circular speed and

centripetal acceleration.

Rotational KinematicsRotational Kinematics

How do we describe an object moving in a circle?

Centripetal ForceCentripetal Force

• A circle follows a curve all the way round and we can describe it quantitatively as well as qualitatively.

• All objects that follow a curved path must have force acting towards the centre of that curve.

• We call this force the centripetal force. (Greek: Centre seeking).

Centripetal accelerationCentripetal acceleration

• Since velocity is speed in a given direction if an object is travelling at a constant speed but is constantly changing direction it must be accelerating.

• This is what is happening in circular motion.

• The acceleration is called Centripetal Acceleration.

Dynamics of RotationDynamics of RotationExamine circular

motion taking Newton’s Laws into consideration.

1st Law-

2nd Law-

3rd Law-

Dynamics of RotationDynamics of Rotation1st Law

• Is Moon at rest?

• Is Moon moving in a straight line?

• Conclusion

MOON

EARTH

Dynamics of RotationDynamics of Rotation1st Law

Objects executing circular motion have a net force acting on them…even if you can’t see the agent of the force.

What force acts on the Moon?

MOON

EARTH

• Earth and Moon orbit the centre of mass of the system.

• Located 1070 miles below the Earth’s surface or 2880 miles from centre of Earth.

Circular velocityCircular velocity

• The instantaneous linear velocity at a point in the circle is usually given the letter v and measured in metres per second (m s-1).

• Speed is defined as the distance / time.•  • For a circle, 1 complete circumference is 2r and

T is the Time period for one rotation (T)• So

v = 2r / T

a = v2/r a is the Centripetal Acceleration. The change in velocity.

OP

Q

v v

Outcomes Outcomes • All should• Be able to define the radian.• Be able to convert degrees into radians and vice-versa.• Most Should• Be able to understand the reasons for using radians.• Be able to solve problems involving a mixture of degrees

and radians.• Some Could• Be able to explain what the idea of centrifugal force is and

why it is imaginary.• Be able to derive the equations for circular speed and

centripetal acceleration.