Rotational Motion Flashcards
Define velocity (v in m.s^-1)
Rate of change of displacement
Define acceleration (a in m.s^-2)
Rate of change of velocity
Define moment of Inertia (I in kg.m^2)
A measure of an object’s resistance to rotational motion about a given axis
Principal of conservation of angular momentum
Total angular momentum before event = total angular momentum after event, provided no external torques are present
Derive v = u + at
a = d^2s/dt^2
S d^2s/dt^2 dt = S a dt
ds/dt = at + k
(t = 0) (k = u)
ds/dt = u
(t = t) ds/dt = v
v = u + at
Derive s = ut + 1/2at^2
v = ds/dt = u + at
S ds/dt dt = S u + at dt
s = ut + 1/2 at^2 + k
(t = 0) (s = 0) (k = 0)
s = ut + 1/2at^2
Derive v^2 = u^2 + 2as
v = u + at
v^2 = (u + at)^2 = (u + at)(u + at)
v^2 = u^2 + 2a(ut + 1/2at^2)
v^2 = u^2 + 2as
What does the gradient of the curve on a motion-time graph represent?
Instantaneous rate of change
What is one full rotation equal to in radians?
2 pi radians
What is one radian in degrees?
57.3 degrees
Define angular velocity (w in rad.s^-1)
The rate of change of angular displacement
Define angular acceleration (a in rad.s^-2)
Rate of change of angular velocity
When an object has an angular velocity, what occurs in its linear motion?
It has a changing linear velocity (due to changing direction) and therefore is accelerating
Angular conversions
s in m > 0 (theta) in radians (rad)
v in m.s^-1 > w (omega) in radians per second (rad.s^1)
u in m.s^-1 > w0 (omega nought) in radians per second (rad.s^-1)
a in m.s^-2 > a (alpha) in radians per second squared (rad.s^-2)
How do we find the area under a line on a graph?
Via integration
Linear conversion equations
s = r0
v = rw
a = ra
Angular velocity and period/frequency equations
w = 2pi/T
w = 2pif
What is meant by centripetal acceleration?
The acceleration toward the centre axis due to circular motion resulting from a centripetal force acting on an object.
What is the equation for centripetal acceleration?
a = v^2/r = r.w^2
What is the equation for centripetal force?
F = m.v^2/r = m.r.w^2
Define torque (t in Nm)
A force which produces rotation about an axis
What is the result of an unbalanced torque?
A change in the rotational motion of an object
What is inertia dependent on?
The distribution of mass about a given axis
Inertia equations
Point mass: I = m.r^2
Rod at centre: I = 1/12m.l^2
Rod at end: I = 1/3m.l^2
Disc at centre: I = 1/2m.r^2
Sphere at centre: I = 2/5m.r^2
