Circular motion: analogous to
linear motion (mostly)
y Tangential speed ~ radius x rotational speed.
y Rotational inertia: mass and mass distribution.
Circular motion: analogous to linear motion (mostly)
Tangential speed ~ radius x rotational speed.
y Speed of an object moving in a circular path:
y Rotational =
= angular: revolutions per sec (rpm’s)
= actual distance covered per second
y -- increases with increasing rpm’s
y
increasing
y --- increases
increases with
with radius
fromradius
centerof path!
y Tangential =
y Torque : causes or stops rotation.
y Centripetal force maintains circular motion.
y vy~-- ω ; v ~ r
y Angular momentum is conserved!
y
Circular motion: analogous to linear motion (mostly) Rotational inertia: mass and mass distribution.
Circular motion: analogous to linear motion (mostly) Torque : causes or stops rotation.
y Getting something to turn:
y Apply force
y Apply force far from rotation axis
y Apply force far from rotation axis, at right angle to radius
y Lever arm = separation of pivot from force
y If force applied parallel to lever arm: no rotation!
y Torque = force * lever arm (force at right angle to arm)
= zero if force parallel to arm
Circular motion: analogous to linear motion (mostly) Centripetal force maintains circular motion.
Circular motion: analogous to linear motion (mostly) : causes to
orturn:
stops
yTorque
Getting something
rotation.
y (Already rotating at constant v : no torque needed.)
y Each mass m being pulled inward: centripetal :
y Apply force
y Apply force far from rotation axis
y Apply force far from rotation axis,Gymnast
at rightAlexei
angleNemov
to radius
“planche”
y Lever arm = shortest distancedoing
fromaforce
direction
y Torque = force * lever arm
y Keep something from turning:
y NET torque = zero (equilibrium)
y F = m v 2/ r
y Caused by various
types of forces:
Palestinian throwing stone at Israelis
using a sling
y Tension, friction,
support forces, …
Banked curve
y Balancing about center of gravity :
y Support must be below the center of mass
Circular motion: analogous to linear motion (mostly) Figure skater
Angular momentum is conserved!
y Angular momentum = “rotational
momentum”
y Extended mass:
rot’l. inertia * rot’l. velocity = I * ω
skater: decreases r , I : rotates faster!
y Point mass m at end of lever arm:
angular momentum = m v r
v = tangential velocity of mass
Sasha Cohen
Circular motion: analogous to linear motion (mostly) Angular momentum is conserved!
y “Rotational inertia”: Rotational 1st Law?
y Angular momentum constant in absence of
net torque.
y Examples: Ice skater, Planet motion…
y Two-dimensional conservation…
y Spinning wheel: rotational speed and
orientation are conserved.
y Bicycle wheel
y Gyroscope