Rotational Motion Flashcards

1
Q

What is meant by Torque (sometimes called the moment of a force)?

A

Torque is the turning effect of a force on a rotating object.

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2
Q

What relationships would you use to convert between:

  1. Linear displacement and angular displacement
  2. Linear velocity and angular velocity
  3. Linear acceleration and angular acceleration
A

For any of these relationships, you would multiply the angular quantity by the radius of circular motion to get the linear quantity:

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3
Q

What does the prefix f stand for?

A

f = femto = x 10-15

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4
Q

How would you find the instantaneous velocity of an object from a displacement-time graph such as this?

A

Take the gradient of the line.

If the graph is a curve, take the gradient of the tangent to the curve at a point.

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5
Q

Which two things does the moment of inertia of an object depend on?

A
  1. The mass of the object
  2. The distribution of mass around a given axis of rotation (which can be quantified with the radius, r)
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6
Q

What does the prefix M stand for?

A

M = mega = x 106

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7
Q

What is the unit of angular displacement?

A

Radians (rad)

[note: rads is incorrect]

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8
Q

What does the prefix G stand for?

A

G = giga = x 109

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9
Q

What does the prefix m stand for?

A

m = milli = x 10-3

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10
Q

How is angular acceleration defined in terms of angular velocity?

A

Angular acceleration is defined as the rate of change of angular velocity.

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11
Q

What is the unit of moment of inertia?

A

kg m2

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12
Q

What does the prefix p stand for?

A

p = pico = x 10-12

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13
Q

How is angular velocity defined in terms of angular displacement?

A

Angular velocity is defined as the rate of change of angular displacement:

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14
Q

What is the unit of Torque?

A

newton-metres (Nm)

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15
Q

What is the unit of angular acceleration?

A

rad s-2

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16
Q

What does the prefix k stand for?

A

k = kilo = x 103

17
Q

What does the prefix P stand for?

A

P = peta = x 1015

18
Q

What is the unit of centripetal acceleration?

19
Q

What is the unit of angular velocity?

20
Q

Convert 360° into radians.

A

360° = 2π radians = 6.28 rad

21
Q

The following experimental setup can be used to determine the moment of inertia of a disc which is allowed to rotate on a frictionless air bearing turntable.

Explain the measurements which will need to be taken, and how to use these to determine the moment of inertia of the disc.

A

Find the torque applied to the disc by using the relationship T = Fr.

Use the light gate to measure the angular acceleration of the disc.

Vary the hanging mass to vary the torque, and repeat a few times.

Plot T against α, and take the gradient of the straight line which will be equal to the moment of inertia of the disc.

22
Q

What is the definition of moment of inertia of an object?

A

The moment of inertia of an object is a measure of its resistance to angular acceleration about a given axis.

23
Q

How would you find the instantaneous acceleration of an object from a velocity-time graph such as this?

A

Take the gradient of the line.

If the graph is a curve, take the gradient of the tangent to the curve at a point.

24
Q

Which two quantities does the rotational kinetic energy of an object depend on?

A

Moment of Inertia and angular velocity

25
What does the prefix **T** stand for?
**T**= tera = **x 1012**
26
What is the unit of angular momentum?
kilogram metres squared per second (kg m2 s-1) (kg m2 rad s-1 also acceptable)
27
Explain the difference between angular, tangential and centripetal acceleration.
* Angular acceleration is the rate of change of **angular velocity** * Tangential acceleration is the rate of change of tangential **speed** * Centripetal acceleration is the rate of change of tangential **velocity-** this causes the direction of the object to change and results in circular motion.
28
What does the prefix **µ** stand for?
**µ** = micro = **x 10-6**
29
A 'conical pendulum' is shown below. In terms of the components of tension in the string determine expressions for the: 1. Centripetal force 2. Weight of the 'bob'.
1. Centripetal force = T sinθ 2. Weight = T cosθ
30
In a 'loop the loop' ride at a funfair, how would you determine the minimum speed required to complete a full loop?
The minimum speed required is when there is no reaction force acting on the 'car', so. Centripetal force = Weight + Reaction force simplifies to Centripetal force = Weight mv2/r = mg **v = √gr**
31
An ice skater is spinning with his arms outward as shown. He then pulls his arms inward. Explain what happens to his angular momentum **and** rotational kinetic energy.
Angular momentum **constant** because angular momentum is always conserved Rotational kinetic energy **increases** because angular velocity increases.
32
What is the unit of tangential acceleration?
**ms-2**
33
A ball of weight W attached to a string is 'whirling' in a horizontal circle as shown below. What provides the centripetal force acting on the ball?
The centripetal force is suppled by the tension, T only. T is the only force acting into the centre.
34
A ball of weight W attached to a string under tension T is 'whirling' in a vertical circle as shown below. Determine a relationship for the centripetal force acting on the ball: 1. at the bottom. 2. at the sides. 3. at the top.
1. Centripetal force = Tension - Weight 2. Centripetal force = Tension 3. Centripetal force = Tension + Weight
35
An expression for the displacement of an object with respect to time is given as s = 3.1t2 + 4.1t + 6 Determine expressions for the object's velocity and acceleration.
**v = 6.2t + 4.1** **a = 6.2 (ms-2)**
36
Describe how to convert an angular velocity in rpm (revolutions per minute) into rad s-1 (radians per second).
revolutions per minute → radians per second: **× 2π** then **÷ 60**
37
State the law of conservation of angular momentum.
**In the absence of external torques**, the **total angular momentum** of object(s) before a collision is equal to the **total angular momentum** of the object(s) after the collision.
38
What does the prefix **n** stand for?
**n** = nano = **x 10-9**
39
Convert 15 revolutions **into radians**.
15 revolutions **= 30π radians = 94.2 rad**