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
Torque equations
t = Fr
t = Ia
Angular momentum (L in kg.m^2.s^-1) equations
L = m.v.r = m.r^2.w
L = I.w
What is the principle of conservation of angular momentum?
The angular momentum before an event = angular momentum after an event, provided no external torque is applied
Kinetic energy equation
Ek = 1/2I.w^2
Potential energy equation
Ep = Ek(lin) + Ek(rot) = 1/2m.v^2 + 1/2I.w^2
What can we observe about centripetal force in a moving vehicle?
When turning, you may slide along the seat. This is because the friction between you and the seat is insufficient to provide central force. Rather than experiencing an outward force, you are in reality continuing in a straight line while the car moves inward.
Where does the centripetal force originate in a conical pendulum?
The horizontal component of tension
What can we observe about centripetal force in an aeroplane banking?
Lift is provided at an angle by the wings, the upward component of lift balances the weight, while the centripetal component causes the plane to turn
What can we observe about Inertia in a figure skater performing a spin?
The skater begins with their arms out, an angular momentum is observed. When they pull their arms in, the angular momentum remains constant. As moment of inertia has decreased, angular velocity must increase, causing a faster spin.
What happens to an object when the torque applied does not cause it to rotate?
It gains kinetic energy
