Torque and Rotational Equilibrium Chapter 8

Torque Rotational equivalent of force Rotational equivalent of force Force isn’t enough to provide a rotation. Force isn’t enough to provide a rotation. Lever arm-distance between where the force is applied and the axis of rotation. Lever arm-distance between where the force is applied and the axis of rotation. Units are Newton meters or Nm Units are Newton meters or Nm Examples: Examples: Doors Doors Wrenches Wrenches Positive and negative correspond to clockwise and counterclockwise. Be consistent. Positive and negative correspond to clockwise and counterclockwise. Be consistent.

Practice A person pushes perpendicular on a door 1.5m from the hinge. If the resulting torque is 277Nm, what force is used? A person pushes perpendicular on a door 1.5m from the hinge. If the resulting torque is 277Nm, what force is used? 47cm 30cm 26N F=? Two thumbtacks are pushed into a record. A string is tied to each thumbtack and each string is pulled to try and turn the record. If the net torque is 6.5Nm clockwise, what is the unknown force? Two thumbtacks are pushed into a record. A string is tied to each thumbtack and each string is pulled to try and turn the record. If the net torque is 6.5Nm clockwise, what is the unknown force? 56 o

Moment of Inertia Measure of an object’s tendency to keep rotating like it’s already rotating. Measure of an object’s tendency to keep rotating like it’s already rotating. Rotational equivalent of mass. Rotational equivalent of mass. Depends on both mass and distance of mass from the center of rotation. Depends on both mass and distance of mass from the center of rotation. The farther the mass from the center of rotation, the bigger the I. The farther the mass from the center of rotation, the bigger the I. Unit is kgm 2 Unit is kgm 2

Various Moments of Inertia All I’s depend on mass and a distance (usually radius) squared. All I’s depend on mass and a distance (usually radius) squared.

Torque and acceleration Newton’s second law can be converted in rotational factors; the relationship stays the same Newton’s second law can be converted in rotational factors; the relationship stays the same A record experiences an angular acceleration of 2.3rad/s 2. If the record has a mass of 753 grams and a radius of 0.31m, how much torque is needed to accelerate the record? A record experiences an angular acceleration of 2.3rad/s 2. If the record has a mass of 753 grams and a radius of 0.31m, how much torque is needed to accelerate the record? A38kg child on a merry go round starts from rest and experiences a 125N force (tangential to the circle) as she sits 1.3m from the center. After she has passed through 25 π radians, how fast will she be going? A38kg child on a merry go round starts from rest and experiences a 125N force (tangential to the circle) as she sits 1.3m from the center. After she has passed through 25 π radians, how fast will she be going?

Equilibrium Both conditions must be met to ensure equilibrium. Since an additional parameter has been set, we can now solve for two variables. For the second condition, you can select the pivot point you want. Select the pivot point so that one of the forces has a lever arm of zero and therefore doesn’t need to be included in the torque equation.

Practice A 1500kg, 20m long metal beam supports a 15,000kg Slurpee 5.0m from the right support. Calculate the force from each leg on the beam. A 55kg girls sits on one end of a 7.8m long seesaw and a 68kg boy sits on the other end. If the seesaw has a mass of 18kg, where should the pivot be in order to have the system balance?

A 4m long board has a mass of 5kg. The book on the left has a mass of 4.2kg and is 0.7m away from the pivot. The book on the right has a mass of 1.1kg and is 1.2m away from the pivot. Find the force of the balloon on the board and the force of the pivot on the board. You may assume the pivot is in the center of the board and the balloon is tied to the end of the board.

Angular Momentum Law of conservation of angular momentum: In the absence of an outside torque, angular momentum is conserved. Like linear momentum, really only important because it’s conserved.

Practice A coin is dropped onto a DVD with a radius of 5cm that is spinning at a rate of 27rev/min. If the DVD has a mass of 17 grams and the coin has a mass of 5 grams, what is the new angular velocity of the DVD? A coin is dropped onto a DVD with a radius of 5cm that is spinning at a rate of 27rev/min. If the DVD has a mass of 17 grams and the coin has a mass of 5 grams, what is the new angular velocity of the DVD? If a gymnast moves from extended to pike position while moving around a bar, how much will her angular speed change assuming she halves her length. If a gymnast moves from extended to pike position while moving around a bar, how much will her angular speed change assuming she halves her length. A girl on a merry go round sits at the outside rim, 3.1m from the center. The merry go round is pushed until it has a rotational velocity of 1.2 rad/s at which time the girl moves inwards so she sits 1.7m from the center. If the girl has a mass of 45kg and the merry go round has a mass of 653kg, what is their final angular velocity? A girl on a merry go round sits at the outside rim, 3.1m from the center. The merry go round is pushed until it has a rotational velocity of 1.2 rad/s at which time the girl moves inwards so she sits 1.7m from the center. If the girl has a mass of 45kg and the merry go round has a mass of 653kg, what is their final angular velocity?

Rotational Kinetic Energy Objects rolling have more KE than objects simply moving in a line. Both need energy to move forward, but the rolling object needs additional energy to move the mass around the middle. An object that is moving forward and moving in a circle will have both regular (translational) kinetic energy and rotational kinetic energy.

Practice Problems A solid steel ball rolls down a 7.8m high ramp. If it starts from rest and has a radius of 12cm, what is its final linear velocity when it reaches the bottom. A solid steel ball rolls down a 7.8m high ramp. If it starts from rest and has a radius of 12cm, what is its final linear velocity when it reaches the bottom.