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Advanced Physics > Rotational Motion > Flashcards

Rotational Motion Flashcards

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1
Q

Define velocity (v in m.s^-1)

A

Rate of change of displacement

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2
Q

Define acceleration (a in m.s^-2)

A

Rate of change of velocity

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3
Q

Define moment of Inertia (I in kg.m^2)

A

A measure of an object’s resistance to rotational motion about a given axis

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4
Q

Principal of conservation of angular momentum

A

Total angular momentum before event = total angular momentum after event, provided no external torques are present

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5
Q

Derive v = u + at

A

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

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6
Q

Derive s = ut + 1/2at^2

A

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

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7
Q

Derive v^2 = u^2 + 2as

A

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

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8
Q

What does the gradient of the curve on a motion-time graph represent?

A

Instantaneous rate of change

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9
Q

What is one full rotation equal to in radians?

A

2 pi radians

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10
Q

What is one radian in degrees?

A

57.3 degrees

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11
Q

Define angular velocity (w in rad.s^-1)

A

The rate of change of angular displacement

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12
Q

Define angular acceleration (a in rad.s^-2)

A

Rate of change of angular velocity

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13
Q

When an object has an angular velocity, what occurs in its linear motion?

A

It has a changing linear velocity (due to changing direction) and therefore is accelerating

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14
Q

Angular conversions

A

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)

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15
Q

How do we find the area under a line on a graph?

A

Via integration

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16
Q

Linear conversion equations

A

s = r0

v = rw

a = ra

17
Q

Angular velocity and period/frequency equations

A

w = 2pi/T

w = 2pif

18
Q

What is meant by centripetal acceleration?

A

The acceleration toward the centre axis due to circular motion resulting from a centripetal force acting on an object.

19
Q

What is the equation for centripetal acceleration?

A

a = v^2/r = r.w^2

20
Q

What is the equation for centripetal force?

A

F = m.v^2/r = m.r.w^2

21
Q

Define torque (t in Nm)

A

A force which produces rotation about an axis

22
Q

What is the result of an unbalanced torque?

A

A change in the rotational motion of an object

23
Q

What is inertia dependent on?

A

The distribution of mass about a given axis

24
Q

Inertia equations

A

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

25
Q

Torque equations

A

t = Fr

t = Ia

26
Q

Angular momentum (L in kg.m^2.s^-1) equations

A

L = m.v.r = m.r^2.w

L = I.w

27
Q

What is the principle of conservation of angular momentum?

A

The angular momentum before an event = angular momentum after an event, provided no external torque is applied

28
Q

Kinetic energy equation

A

Ek = 1/2I.w^2

29
Q

Potential energy equation

A

Ep = Ek(lin) + Ek(rot) = 1/2m.v^2 + 1/2I.w^2

30
Q

What can we observe about centripetal force in a moving vehicle?

A

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.

31
Q

Where does the centripetal force originate in a conical pendulum?

A

The horizontal component of tension

32
Q

What can we observe about centripetal force in an aeroplane banking?

A

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

33
Q

What can we observe about Inertia in a figure skater performing a spin?

A

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.

34
Q

What happens to an object when the torque applied does not cause it to rotate?

A

It gains kinetic energy

Advanced Physics (5 decks)

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