torque and rotational motion unit 7 Flashcards
Rotational motion
the movement of an object that spins around an axis
ex. pinwheels, the spinning of the earth, etc.
Angular position
the degree of the object from the axis’s horizontal point
Measured in radians
Arc length
the distance the particle or object has traveled along its circular path
Variable = s
Eqn for radians
radians = s/r
Revolution
When a particle makes a full movement around the circle. Radian (1 Revioltion) = 2pi rad
Angular Velocity
the angular displacement over a period of time. Particles w higher angular velocity will undergo higher angular displacement during uniform circular motion.
Variable = w
Eqn for angular velocity
w = angular displacement/time
Angular displacement for unifrom circular motion
Of = Oi = ONET = w*t
Angular speed
the absolute value of the angular velocity.
= 2pi rad/T
Linear and angular speed
v=wr
Rigid body
a body that maintains a constant shape
Rigid body velocity
All points thorughout the rigid body object in uniform circular motion have the same angular velocity but different linear velocities
angular acceleration
the rate of change of angular velocity
Eqn for angular acceleration
w/t
Linear and circular motion
Switch x with rad, v with w, and a with alpha to convert the linear motion eqns into circular motion eqns
(CAAKE)
Tangential Acceleration
the component of acceleration at the tangent point of the circle
Eqn for tangential acceleration
a= wr/t or a = alpha * radius
Torque
the rotational equivalent of force
Eqn for torque
T= r F sin theta
Radial Line
the line starting at the pivot and extending through the point at which the force is applied
Moment Arm
the perpendicular distance from a reference point to the line of action of the force
Positive and negative torque
+ will be in the CCW direction while
- will be in the CW direction
Center of Gravity
the point where the net force of gravity acts on an object
Torque and angular acceleration
torque causes angular acceleration a=t/mr^2
Moment of inertia
l=m1r1^2+m2r2^2+m3r3&2+…
Newton’s second law of rotation
a=tnet/l
Moment of inertia is the rotational equivalent of
Mass
Rolling motion
A combination motion where an object moving about an axis is also moving in for a straight line. For an object that moves without slipping, v=wR
