Circular MotionCircular Motion

Rotation and RevolutionRotation and Revolution

When a body turns about it’s axis is When a body turns about it’s axis is known as a known as a rotationrotation..– A skater spins about their axis.A skater spins about their axis.

When a body turns about an external When a body turns about an external axis is known as a axis is known as a revolutionrevolution..– A Merry Go Round rotates while the A Merry Go Round rotates while the

riders on the ride revolve around the riders on the ride revolve around the Merry Go Round.Merry Go Round.

Rotational SpeedRotational Speed

Tangential SpeedTangential Speed– Speed of a point around the circumference of a Speed of a point around the circumference of a

circular path.circular path. Speed varies according to the distance from the axis.Speed varies according to the distance from the axis.

– Points farther away from the axis have a higher Points farther away from the axis have a higher tangential velocity than points closer the axis because tangential velocity than points closer the axis because they have a larger distance to cover.they have a larger distance to cover.

Angular speedAngular speed– Number of rotations in a given amount of time.Number of rotations in a given amount of time.

Rotations per minute.Rotations per minute. All points on a rigid circular object have the same All points on a rigid circular object have the same

angular speed.angular speed.

Centripetal ForceCentripetal Force

Any force that causes an object to follow a Any force that causes an object to follow a circular path.circular path.– Types of Centripetal ForcesTypes of Centripetal Forces

GravityGravity – Keep Satellites in orbit. – Keep Satellites in orbit. TensionTension – Pull on a string keeps a ball in a circular path. – Pull on a string keeps a ball in a circular path. FrictionFriction – The tires experience and inward force of friction – The tires experience and inward force of friction

to keep a car from skidding sideways around a turn.to keep a car from skidding sideways around a turn. Normal ForceNormal Force – The supporting force of a car door when a – The supporting force of a car door when a

car travels around a sharp curve.car travels around a sharp curve.

– Without centripetal forces the objects would Without centripetal forces the objects would continue to move straight ahead tangent to the continue to move straight ahead tangent to the circular path.circular path.

Without a centripetal force the Without a centripetal force the object continues on a straight object continues on a straight

path.path.

Center of GravityCenter of Gravity Point in which most of the weight is centered in Point in which most of the weight is centered in

an object.an object.– Sometimes called the center of mass.Sometimes called the center of mass.– For a symmetrical object the center of gravity is its For a symmetrical object the center of gravity is its

geometric center.geometric center.– For irregular shaped objects its where most of the mass For irregular shaped objects its where most of the mass

is concentrated.is concentrated. An object tends to rotate around the center of An object tends to rotate around the center of

gravity as if it were a stationary point.gravity as if it were a stationary point.– It is the balance point that supports the entire object.It is the balance point that supports the entire object.– The center of gravity can also exhist where there is no The center of gravity can also exhist where there is no

material at all. For example a hollow sphere has the material at all. For example a hollow sphere has the center of gravity at its geometric center.center of gravity at its geometric center.

A ball will tend to roll so that its center of gravity A ball will tend to roll so that its center of gravity is as low as possible to the ground.is as low as possible to the ground.

Toppling and Center of Toppling and Center of GravityGravity

If the center of gravity is above the If the center of gravity is above the area of support the object will remain area of support the object will remain upright.upright.– The leaning tower of Pisa does not The leaning tower of Pisa does not

topple because the center if gravity topple because the center if gravity does not extend beyond is support base.does not extend beyond is support base.

Rotational MechanicsRotational Mechanics

TorqueTorque– Force applied to an object that makes it Force applied to an object that makes it

rotate.rotate.– Torque is produced when a force is Torque is produced when a force is

applied with leverage.applied with leverage. The longer the handle the more leverage.The longer the handle the more leverage. The force must be applied perpendicular to The force must be applied perpendicular to

the pivoting point.the pivoting point. The lever arm is the distance between the The lever arm is the distance between the

pivot point and the force applied.pivot point and the force applied.– Torque = length of lever arm x force Torque = length of lever arm x force

(perpendicular)(perpendicular)

Balanced Torques Balanced Torques

A balanced teeter totter represents A balanced teeter totter represents balanced torques because the balanced torques because the clockwise rotation equals the clockwise rotation equals the counterclockwise rotation.counterclockwise rotation.

Torque and center of gravity. If you Torque and center of gravity. If you stand with your back to the wall and stand with your back to the wall and try to touch your toes you will rotate.try to touch your toes you will rotate.– Your center of mass is not over your Your center of mass is not over your

base so you topple over.base so you topple over.

Rotational InertiaRotational Inertia

An object rotating about its axis will An object rotating about its axis will continue to rotate about its axis.continue to rotate about its axis.

The resistance to a change in rotation is The resistance to a change in rotation is called called rotational inertia rotational inertia sometimes called sometimes called moment of inertia.moment of inertia.– Torque is required to change the rotational Torque is required to change the rotational

inertia of an object.inertia of an object.– Depends on the distribution of mass.Depends on the distribution of mass.– Greater distribution of mass more roatational Greater distribution of mass more roatational

inertia.inertia. In other words if the mass is distributed around the In other words if the mass is distributed around the

edges of the object it is more difficult to rotate.edges of the object it is more difficult to rotate.

Angular MomentumAngular Momentum

Angular momentum is product of Angular momentum is product of rotational velocity and rotationla rotational velocity and rotationla inertia.inertia.

Angular momentum is a vector that Angular momentum is a vector that acts along the axis of rotation.acts along the axis of rotation.