Physics - Topic Test 1

Torque

If torque is applied to an object, it can cause the object to rotate about a pivot → also referred to as a moment

a force that tends to cause rotation.

Torque equation

rf sin x = Torque

Torque = Nm

r = distance rom the pivot to the point @ which force acts w/ units of metres (m)

F = applied force with units of N

x = angle between the line joining the pivot to the point @ which the force acts + direction of force

Key notes about Torque:

• Torque is maximised when it is applied at a right angle to the lever arm

• Direction of torque is direction of rotation

When turning effect is applied, there must be factors that work together

1. Pivot point around which an object will rotate → axis of rotation

2. Force → applied to the object in a way to cause the object to rotate: not applied through pivot point

3. Line of action → must not be passed through the pivot point

Another formula for Torque

• T = r† F

r† = the perpendicular distance from pivot to force’s line of action

Translational Equilibrium

• ∑F = 0 → no net force acts on it

• when sum of forces acting through centre of mass equals zero

• * not all forces act through centre of mass → some forces act in ways that generate torque/moment on an object

Vertical + horizontal forces

• It is convenient to analyse the vertical and horizontal forces seperately

• ∑Fy=0, ∑Fx=0

Rotational equilibrium

• ∑t = 0 → if no net torque acts upon it

• A useful way to analyse rotational equilibrium is by stating that CW = ACW

Static eqilibrium

• no net force and no net torque acts on it

• ∑f = 0, ∑t = 0

Conditions for static equilibrium

• must be in both translational + rotational equilibrium

• must not be accelerating or rotating

• Cantilevers, struts + ties

Stability can be increased by:

• lowering centre of gravity

• width of support base ⬆

• angle from centre of gravity to edge ⬆

Principle of moments:

• sum of moments in a clockwise direction must balance the sum of moments in an anticlockwise direction for an object to be in rotational equilibrium

stable, unstable and neutral equilibrium

• stable: stay even when a force is acted on it (if centre of mass is not @ base of support)

• unstable: object will accelerate and not return to equilibrium position when a force is applied: centre of mass is moved outside of base of support

• neutral equilibrium: object will remain stationary no matter where it is placed → any force has no effect on relationship between centre of mass + base/point of support.

Circular motion

• If a car is travelling in a straight line at a constant speed there is no net force acting on it

• If a car is travelling in a straight line at a constant speed, but is turning a corner, its direction is changing

  • velocity → a change in direction = change in velocity

  • a change in velocity → acceleration + a net force

• The turning car is undergoing acceleration even though its speed is constant

Period + Frequency

For an object to be travelling at a constant speed, v, around a circle of radius r, it will take T seconds to compete a single revolution

• T = period

frequency is the number of rotations per second

• Hz

Uniform Circular Motion

• If an object is moving around a circle of radius r in a period of time T, its speed can be defined as

• speed is constant, velocity is always changing (and at any instant, tangential)

V = circumference/period= distance/time = (2 x pi ) / r

Acceleration

• If the v of the object is changing direction, not magnitude, it must be accelerating.

• It is continually deviating inwards from its straigh line motion and has an acceleration directed towards the centre (but it never gets any closer)

• Centripetal Acceleration can be defined as Ac = v²/r = (4xpi²r)/T²

Centripetal Force

This force is responsible for constantly changing the direction of the object's velocity, keeping it in a circular path.

Fc = mAc = (mv²)/r = (m^4 pi² r)/T²

Forces that cause circular motion

• Newton 2 → hammerball is continually accelerating, therefore must have net force and unbalanced force acting on it

  • the net unbalanced force continuously acting on it gives the hammer ball its acceleration towards the centre of the circle = centripetal force

• a real force acting on the object is necessary to provide centripetal force

  • (e.g. friction, gravity, tension)

  • acts in direction of acceleration

• once released, acts in a straight line tangential to circular path

• centrifugal force → upwards Ff to counteract gravity

• totem tennis → can never be flat as there must be a V force

Various Scenarios:

An object being whirled around → will always have a vertical tension component that is equal to the weight force of the object (assuming we are in generational field)

Ty = mg

Tx = Tcosθ

therefore Tcosθ = (mv²)/r

Going around a banked corner

a vehicle going around a banked corner will have a normal force that has a horizontal component, which provides the centripetal force

therefore Ttanθ = (mv²)/r

Leaning into a corner

In leaning over, they are introducing a horizontal reaction force in addition to the normal force, creating a reaction force from the road that is at an angle - it is the horizontal component that provides the centripetal force.

therefore F net = Fc = mgtanθ = (mv²)/r

Vertical Circular Motion

• If a vehicle is undergoing circular motion in the vertical plane (in a grav. field) we need to account for weight force at different points in the loop

Various scenarios: At the top of the hill

F net = mg - N

=mg-Fnet

=mg-Fc

= mg - (mv²/r)

At the bottom of a hill

F net = N- mg

=mg+Fnet

=mg+Fc

= mg + (mv²/r)

At the top of a loop

F net = mg + N

= Fnet - mg

= Fc - mg

= (mv²/r) - mg

therefore, need to have mv² > (or equal to) mg or will fall out of seat

Banking

enables vehicles to travel at higher speeds w/o skidding, especially over ice

• it is at some angle to the horizontal

• e.g. Velodromes NASCAR

• roads are designed to be banked in places w/ sharp corners e.g. exit ramps on freeways

cars rely n force of friction between tyres + road to provide sideways force that keeps the car turning in a circular path

reduces the need for sideways Ff required for a car to turn + vehicles can go faster around corners

Normal force is greater on a banked track than a flat track

Design speed

• the car travels at a speed at which there is no sideways Ff required to take the curve

  • dependent on the angle at which the track is banked

  • car exhibits no tendency to ‘drift,’ maintaining circular radius

• When travelling @ design speed, car still has acceleration towards the centre due to bamkingg, there are only 2 forces on the car

  • Fg and Fn → res force = horizontal, directed towards C

Leaning into corners

• the rider is travelling in a horizontal circular path @ constant speed, they experience a centripetal acceleration directed towards the centre of the circle (therefore not force too)

Turning in flight

• Normal force is replaced by lift force

  • when making turns, aeroplanes + birds must ⬆ life force (because they need to tilt) directed towards centre to maintain height

Moving in vertical circles

• at the top + bottom → neither speed up/down → acceleration is purely centripetal

Travelling through dips →

centripetal acceleration if vertically upwards, net centripetal force is upwards, ∴FN and Fg are not balanced anymore

FN + Fg = Fc

Travelling over humps

• Centripetal acceleration is downwards

• Net Centripetal force is downwards

• Fg + FN = FC = _N downwards

  • **Fg must be greater than 80N downwards

  • this amounts to less than normal force that usually acts, explaining why you feel the seat pushing against you less strongly → reduces apparent weight

• Fg remains constant the whole ride, normal force varies

Vertical loops

• moves on the underside of the track, and FN still acts towards the tracks surface, meaning it acts downwards relative to the ground, but up relative to the rider

  • Fn and Fg provide centripetal force

Non uniform speeds on rollercoaster rides

when descending, GPE ⬇ and KE ⬆ → feel heavier

@ higher speeds: a greater centripetal acceleration is required to maintain circular motion

• speed must exceed a critical threshold to ensure cart remains securely on the track

  • LAW OF CONSERVATION OF ENERGY → mechanical energy remains the same

• people do not fall out as their centripetal acceleration is greater than acceleration due to gravity, and continually exerting a normal force