Circular Motion and SHM Flashcards by Daniel Mawson

What is the term given to an object rotating at a steady rate?

Uniform circular motion

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If an ball on a string is travelling in a circle in the vertical plane, where are the points of minimum and maximum tension?

Minimum tension at the top
Maximum tension at the bottom

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Define centripetal force

The resultant force that makes the object move in a circle

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Why do planes turn when at an angle?

The lift force is comprised of a horizontal and vertical component.
The horizontal component provides the centripetal force causing it to turn.

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What kind of motion will a pendulum perform?

Simple harmonic motion

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What is the period of oscillation?

The time for one complete cycle of oscillation.

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If the graph of displacement is sin(x), what will the respective graphs of velocity and acceleration look like?

Velocity as cos(x)
Acceleration as -sin(x)

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Describe a freely oscillating object

It oscillates with a constant amplitude because there is no friction acting on it.

(Its energy is constant)

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What is natural frequency?

The frequency of free oscillations of an oscillating system.

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What are forced vibrations?

Making an object oscillate at a frequency that is not it’s natural frequency

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When does resonance occur?

When the frequency of driving force or oscillation matches the natural frequency of the system.

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What is the outcome of resonance?

An increase in amplitude of the system’s oscillation.

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What is damping?

The term used to describe the removal of energy from an oscillating system.

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What are the three levels of damping?

Light
Heavy
Critical

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Describe light damping of a system

The system oscillates over a long time frame before coming to rest.
The amplitude of the oscillations exponentially decay.

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Describe heavy damping (over damping)

System not allowed to oscillate.

Slowly returns to equilibrium.

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Describe critical damping

The oscillating system returns to the zero position of the oscillation after one quarter of a time period.

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How do you convert degrees -> radians

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How do you convert radians -> degrees

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Define angular displacement

The angle through which an object in circular motion travels in a given time

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How do you deal with rpm? (revolutions per minute)

÷60 to convert to rps (revolutions per second)

Then set rps = frequency

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Define frequency

The number of complete oscillations per second

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What is the equation for linear velocity?

Why is an object in circular motion accelerating?

Its linear velocity does not change in magnitude

But is constantly changing in direction

In circular motion which direction do the acceleration and centripetal force vectors act?

**Always towards the centre**

What is the condition for circular motion to happen?

A **velocity** needs to be acting **perpendicular** to a **resultant force**

What happens if... F_centri\> F_max

Circular motion does not happen (Eg car skids off the road or moves to a higher radius)

What happens if... F_centri max

Circular motion happens (eg friction is large enough to keep car on track)

What is F_centrifor an object at the top of the vertical circle?

What is F_centri for an object on top of a vertical circle?

What is F_centri for an object at the bottom of a vertical circle?

How do you find out the minimum velocity for an object travelling in a vertical circle?

Set R=0 (or tension if ball on string) And rearrange for v

How do you find out the maximum velocity for an object travelling over a vertical circle? (eg car over a hill)

Set reaction R=0 Then rearrange for v

When solving angled circular motion problems what are the 3 usual steps?

1. Set vertical component of force = weight 2. Work out horizontal component using trig 3. F_centri = horizontal component

Why can't a ball be swung around in a circle **with the string horizontal?**

There must be a vertical component of the tension to match the weight Otherwise ball is not in vertical equilibrium

What are the **two conditions for SHM?**

1. Acceleration must be proportional to displacement 2. Acceleration must be opposite to displacement

How does the time period differ for the two pendulums?

**Time period is independent of amplitude**

Define amplitude.

The **maximum displacement** of an obejct/particle/point **from equilibrium position**

Label up the maximum and minimum velocities and accelerations on the simple pendulum...

Label up the maximum and minimum velocities and accelerations on the mass spring system...

Label up the maximum and minimum potential and kinetic energies on the simple pendulum...

What are the kinetic energy, potential energy and total energy lines for one cycle of SHM?

When do you use? x=Acos(wt) When do you use? x=Asin(wt)

x=Acos(wt) -\> displacement in SHM when x=A when t=0 x=Asin(wt) -\> displacement in SHM when x=0 when t=0

How do you calculate KE_max or PE_max or E_T in SHM?

What two factors affect the time period of a mass spring system in SHM?

1. Mass on the end of the spring 2. Spring constant (stiffness) of spring

What two factors affect the time period of a mass spring system in SHM?

1. Length between top of string and centre of bob 2. Gravitational field strength

What does the graph of energy against displacement look like in SHM?

Does circular motion count as SHM?

When projected onto a flat surface, yes it does

When an SHM system is **lightly damped** what happens to its **amplitude and time period?**

Amplitude decreases (as it loses energy) But time period remains constant

How is natural frequency determined for a mass spring system?

How is natural frequency determined for a simple pendulum?

What happens if the frequency of driving force is less than the natural frequency of a system? f0

Low amplitude oscillations With 0 phase difference.

What happens if the frequency of driving force matches the natural frequency of a system? f=f₀

**Resonance occurs** Large amplitude oscillations π/2 radians out of phase

What happens if the frequency of driving force is more than the natural frequency of a system? f\>f₀

Low amplitude oscillations With phase difference of π

The graph below shows driven oscillations with varying frequencies. Add two lines if the system is: 1. Undamped (free oscillations) 2. Over damped

For Barton's pendulum which two balls oscillate?

P and Y because they have the **same length** So **natural frequency of y matches** frequency of driving force from **P**