Circular Motion

Rotation and Revolution When a body turns about it’s axis is known as a rotation. When a body turns about it’s axis is known as a rotation. –A skater spins about their axis. When a body turns about an external axis is known as a revolution. When a body turns about an external axis is known as a revolution. –A Merry Go Round rotates while the riders on the ride revolve around the Merry Go Round.

Rotational Speed Tangential Speed Tangential Speed –Speed of a point around the circumference of a circular path.  Speed varies according to the distance from the axis. –Points farther away from the axis have a higher tangential velocity than points closer the axis because they have a larger distance to cover. Angular speed Angular speed –Number of rotations in a given amount of time.  Rotations per minute.  All points on a rigid circular object have the same angular speed.

Centripetal Force Any force that causes an object to follow a circular path. Any force that causes an object to follow a circular path. –Types of Centripetal Forces  Gravity – Keep Satellites in orbit.  Tension – Pull on a string keeps a ball in a circular path.  Friction – The tires experience and inward force of friction to keep a car from skidding sideways around a turn.  Normal Force – The supporting force of a car door when a car travels around a sharp curve. –Without centripetal forces the objects would continue to move straight ahead tangent to the circular path.

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

Center of Gravity Point in which most of the weight is centered in an object. Point in which most of the weight is centered in an object. –Sometimes called the center of mass. –For a symmetrical object the center of gravity is its geometric center. –For irregular shaped objects its where most of the mass is concentrated. An object tends to rotate around the center of gravity as if it were a stationary point. An object tends to rotate around the center of gravity as if it were a stationary point. –It is the balance point that supports the entire object. –The center of gravity can also exhist where there is no material at all. For example a hollow sphere has the center of gravity at its geometric center. A ball will tend to roll so that its center of gravity is as low as possible to the ground. A ball will tend to roll so that its center of gravity is as low as possible to the ground.

Toppling and Center of Gravity If the center of gravity is above the area of support the object will remain upright. If the center of gravity is above the area of support the object will remain upright. –The leaning tower of Pisa does not topple because the center if gravity does not extend beyond is support base.

Rotational Mechanics Torque Torque –Force applied to an object that makes it rotate. –Torque is produced when a force is applied with leverage.  The longer the handle the more leverage.  The force must be applied perpendicular to the pivoting point.  The lever arm is the distance between the pivot point and the force applied. –Torque = length of lever arm x force (perpendicular)

Balanced Torques A balanced teeter totter represents balanced torques because the clockwise rotation equals the counterclockwise rotation. A balanced teeter totter represents balanced torques because the clockwise rotation equals the counterclockwise rotation. Torque and center of gravity. If you stand with your back to the wall and try to touch your toes you will rotate. Torque and center of gravity. If you stand with your back to the wall and try to touch your toes you will rotate. –Your center of mass is not over your base so you topple over.

Rotational Inertia An object rotating about its axis will continue to rotate about its axis. An object rotating about its axis will continue to rotate about its axis. The resistance to a change in rotation is called rotational inertia sometimes called moment of inertia. The resistance to a change in rotation is called rotational inertia sometimes called moment of inertia. –Torque is required to change the rotational inertia of an object. –Depends on the distribution of mass. –Greater distribution of mass more roatational inertia.  In other words if the mass is distributed around the edges of the object it is more difficult to rotate.

Angular Momentum Angular momentum is product of rotational velocity and rotationla inertia. Angular momentum is product of rotational velocity and rotationla inertia. Angular momentum is a vector that acts along the axis of rotation. Angular momentum is a vector that acts along the axis of rotation.