Circular Motion Torque

What We Want to Know… What is torque? What variables influence torque? What is required for torque to be balanced? What is an objects center of mass? What are machines and why use them?

What is Torque? Torque (τ) is a measure of the ability of a force to rotate an object about an axis Torque causes rotation Depends on the magnitude of the force the direction of the force the lever arm

Mathematically… Units are Newton·Meters (N·m) Similar to Work

Torque (cat door) Torque depends on the direction of the force compared to the lever arm The greatest torque occurs when the Force is perpendicular to the lever arm Demonstrate with students at door

Torque Torque = Force x Lever Arm Lever Arm is the perpendicular distance from the Force to the Axis of Rotation Greater the lever arm… the greater the torque Discuss “force to axis of rotation”, “perpendicular distance”

Torque Torque is a vector with magnitude and direction Positive torque produces counter-clockwise rotation Negative torque produces clockwise rotation Thumb along the lever arm with fingers curving in the direction of the force. Right hand rule… Thumbs up- positive Thumbs down- negative

Net Torque Since there can be more than one force on an object, there can be more than one torque Net Torque is the sum of all torques acting on an object or system a=2m b=4m Torque = force x distance Net torque = 12N x 2m – 10N x 4m – 9N x 4m = 24 N-m - 40N-m - 36N-m = -52 N-m

Axis of rotation/ fulcrum Balanced Torque What is the net torque of the see-saw? What happens? The object will not rotate… it’s balanced What if the object is already rotating? Axis of rotation/ fulcrum 15 5 30m 10m

Torque… Doorknobs are normally placed on the edge of doors. How much more force would be required to open the door if it was in the center of the door?

Torque… Which is easier for turning a stuck screw, a long handled screw driver or one with a fat handle? Which makes it easier to pry a lid off a paint can? Greater the lever arm… greater the torque Axis of rotation Axis of rotation Lever arm Lever arm

Equilibrium Complete Equilibrium requires the net force and the net torque to be zero

Center of Mass (Gravity) When gravity is the only force… All objects have one point where the net torque is zero… This point is called the center of mass. Center of Mass Mg mg

Center of Mass (Gravity) Unless restrained, all objects will rotate around their center of mass Objects will move as if all their mass is concentrated at the center of mass (hence the name) Motion of a 3-D object is a combination of: Rotation around the center of mass Movement (translation) of the center of mass

Center of Mass (Gravity) Objects balance when the net force acts through their center of mass.

Try This… Stand straight facing a wall with your toes touching the wall. Try to stand on your toes. Stand with your back and heels touching the wall. Try to bend forward.

Toppling An object will topple (fall over) if the CG is not directly over a support

Try This… Stand straight facing a wall with your toes touching the wall. Try to stand on your toes. Stand with your back and heels touching the wall. Try to bend forward. Sitting in your chair, try to stand up with out bending.

Stability Stability is resistance to toppling… The lower the Center of Mass, the more stable the object Stable equilibrium…(bowl) Unstable equilibrium…(balanced rod) Neutral equilibrium…(ball)

Machines Machines ease our load by making tasks easier… we use them everyday In general, Machines decrease the force required to complete a task (do Work) Some machines may change the direction of the force required to do work in another direction

Simple Machines Machines, no matter how complex, are combinations of one or more of six simple machines Compare force and movement of “regular lift” to “pulley lift” to “inclined plane”

Mechanical Advantage output force MA = input force dout MA = din The whole idea is to decrease the force required to do a given amount of Work Input force less than Output force Mechanical Advantage is a measure of a machines effectiveness and is the ratio of the output force to the input force The greater the MA, the more effective the machine output force MA = input force dout MA = din

Efficiency Wout ____ effeciency = X 100% Win Under actual conditions friction is a factor Some energy (work) will be “lost” Output work will be less than the Input work The efficiency of a machine is a measure of how well a machine accomplishes its task Defined as the ratio of output work to input work Efficiency can be written as… Wout ____ effeciency = X 100% Win

Practice problems Via the worksheet

Machines What is the mechanical advantage of a pulley that can raise a 80 N box by applying a 12 N force? If a machine has an efficiency of 55%, how much work would be done by 400 J with that machine? MA = 6.67 Wout = 220 J

Examples What is the torque produced by a 10N force applied to a door 0.5m from the hinge? Calculate the torque due to gravity on a 3.0kg simple pendulum attached to a 1 meter long string at 10, 30, and 45 degrees from it’s at rest position. At what angle is the torque at its maximum? Ended here in Physics

Practice A teeter-totter is 3.0m long with the fulcrum in the middle. You notice that your friend has to sit 0.25m from one end with you on the other to balance the teeter-totter. If your mass is 45kg what is the mass of your friend? A meter stick has a 2.0kg mass on one end and a 5.0 kg mass on the other. Where would you place your finger to balance the meter stick? m = 54 kg At 0.286 m or 0.714 m

Circular Motion A spool of wire is being wound clockwise by a 20 N force applied 0.6 m from the center. The wire itself is resisting with a counter-clockwise pull of 7.0 N applied 0.2 m from the center. What is the net torque on the spool? Στ = -10.6 N·m

Circular Motion 20.0 kg Mindy walks onto a support beam hanging 2.0 m off the edge of a building. Buttons grabs the other end of the beam which is 3.0 m away from the edge. What is the minimum force Buttons needs to apply to keep Mindy from falling? FButtons = -130.8 N

Circular Motion Mars’ moon Deimos is 23,459 km from Mars. What is the force of gravity between Mars and its moon? The mass of Mars is 6.42 x 1023 kg and the mass of Deimos is 4.96 x 1015 kg. What is the average speed of Deimos around Mars? Fg = 3.86 x 1014 N v = 1350.77 m/s