Lesson 9: Fixed Axis Rotation Flashcards
Define:
fulcrum and lever arm
The fulcrum is the point of an object that remains fixed during rotation.
The lever arm is the distance from the fulcrum where a force is applied, to create rotation around the fulcrum.
Define and give units for:
torque
Torque is the ability of a force to create a change in the angular orientation of an object, by rotation about a fulcrum point. Torque can also be thought of as the component of work perpendicular to a lever arm.
The SI unit of torque is the N-m.
Describe the relationship between the lever arm radius and force applied, which leads to torque.
τ = r*F sinθ
Where r is the distance between force applied and the fulcrum point, F is the magnitude of force applied, and θ is the angle between the lever arm and the force vector.
Only the component of force perpendicular to the lever arm will generate torque, since:
sin(0) = sin(180) = 0.
How will the torque on a lever arm change, if the same force is applied half the original distance from the fulcrum?
Torque will be halved.
Since torque = r*F sinθ, torque is directly proportional to the distance along the lever arm. Halving the distance that the force is applied at will halve the torque as well.
Describe the convention of rotation that is exhibited from a positive torque.
Counter-clockwise rotation is positive torque.
The maximum positive (counter-clockwise) torque that a force can deliver is at 90 degrees to the lever arm.
Describe the convention of rotation that is exhibited from a negative torque.
Clockwise rotation is negative torque.
The maximum negative (clockwise) torque that a force can deliver is at 90 degrees to the lever arm.
Define:
rotational equilibrium
Rotational equilibrium occurs when the net torque on an object is zero. If the sum of all torques acting on an object cancel to zero then the object will not undergo rotational acceleration.
A child on a see-saw leans back, causing her to to lower and her partner to rise. Is the see-saw system in rotational equilibrium?
No, the see-saw is experiencing changing rotation, which must be due to a non-zero net torque, hence there is not rotational equilibrium.
A child of mass 40kg sits 1.5m from the pivot of a see-saw. To balance exactly, where on the opposite end should her 30kg little sister sit? (assume the seesaw is massless)
She should sit 2m from the pivot point.
Since all forces due to gravity are perpendicular to the see-saw, torque from the 40kg child will be: (mg)r = 40(10)(1.5) = 600 Nm. To balance, the 30kg child needs to supply 600 Nm of torque, which requires a distance of 2m.
