ROTATIONAL DYNAMICS

Section 8. 2

Rotational Dynamics• How can I describe torque?

• What factors influence torque?

Opening A Door• Easiest Way to do it?

• Why is the handle where it is?

Opening a Door

Rotational Dynamics

• A force must be exerted to open a door

• Doorknob is near the outer edge, as far from the axis of rotation as possible

• Pull at a right angle to the door to apply the most force

Rotational Dynamics

• So where we apply the force changes how effective it is

• In this section we will be measuring how effectively an applied force turns something

• Pertains to doors, pedals, wrenches…..

Rotational Dynamics• The change in angular velocity depends on:

• the magnitude of the force• the distance from the axis to the point where the force is exerted • the direction of the force

Lever Arm

• Lever Arm: The perpendicular distance from the axis of rotation to the point where the force is exerted

Lever Arm

• For the door, it is the distance from the hinges the point where you exert the force

• If the force is perpendicular to the radius of rotation then the lever arm is the distance from the axis, r

Reduced Lever Arm

• If force is not perpendicular, lever arm is reduced

• Lever Arm (L)

• L = r sin ɵ

• ɵ = angle between force and the radius from the axis of rotation to the point where the force is applied

Torque

• Torque: How effectively a force causes rotation

• – tau

• Measured in Newton meters

Example

• A bolt on a car engine needs to be tightened with a torque of 35 Nm.

• You use a 25 cm long wrench to pull on the end of the wrench at an angle of 60.0° from the perpendicular.

• How long is the lever arm and how much force do you have to exert?

Homework• Page 203• # 11 - 15

Balancing Torques• http://phet.colorado.edu/en/simulation/balancing-act

When we played with the balance, what two things did we change?

Moment of Inertia• Moment of Inertia: Resistance to rotation of a point mass

• Symbol = I

• Units kg·m2

Moment of Inertia

• Hold your book at the bottom and rotate

• Hold your book in the middle and rotate

• Which one has a lower torque?

Moment of Inertia• When something is spinning, we have not taken into account shape

Homework• Read Page 205-207