Torque and Rotational Kinematics

Torque

Measure of the ability of the force to cause rotation/ Measurement of a ROTATION caused by a FORCE

Lever arm

The PERPENDICULAR DISTANCE between the FULCRUM & the point of application of the FORCE

Fulcrum/ pivot point

Point of ROTATION *turning point of a wrench

Torque Equation

Torque (Nm) = force (N) * lever arm (m)

or

T=rFsin(theta)

torque units

Nm(Newton-meters)

Torque is affected by

-the magnitude of force applied

-length of lever arm from axis of rotation to point of force application

-orientation of the line of action of the force (angle between the two)

what determines the amount of torque

the amount of force applied, the angle the force is applied at,

And

The distance from the pivot point that the force is applied at.

torque acting on an object tends to produce

rotation

Clockwise rotation

Negative torque

counter clockwise rotation

Positive torque

equilibrium

a steady state due to the equal action of opposing forces

How much torque is created by applying 20 N of force to a 1.6 m wide door?

32 Nm

The total length of the see-saw is 8m. Stefani is at the very end of the see-saw with a weight of 360 N. The second child (Stefan) has a mass of 790 N. The see-saw is balanced. What is the net torque?

0 Nm

The total length of the see-saw is 8m. Stefani is at the very end of the see-saw with a weight of 360 N. The second child (Stefan) has a mass of 790 N. Where should Stefan sit to balance Stefani's torque?

1.82 m from the center

Translational Equilibrium

The sum of the forces is equal to 0.

Rotational Equilibrium

The sum of all the torques is equal to 0.

When torque equals zero the object undergoes

angular acceleration

angular displacement equation

theta = arc length/radius

Angular Displacement

During time t, the reference line moves through angle θ

ω

angular speed

α

angular acceleration

Relationship between Angular and Linear Velocity

v = ω r

Relationship between Angular and Linear acceleration

a = α r

2π radians

360 degrees, 1 circle, 1 revolution

if angular velocity (ω) and angular acceleration (α) are in the same direction (both __________ and _________ or both _________ and __________) then object ___________

counterclockwise, positive, clockwise, negative, speeds up

if angular velocity (ω) and angular acceleration (α) are in opposite directions direction (one __________ and _________ and the other _________ and __________) then object ___________

counterclockwise, positive, clockwise, negative, slows down

rpm

revolutions per minute

angular position/displacement, angular velocity, and angular acceleration are all _________ that have a _________ and ___________

vectors, magnitude, direction