Physics - Circular Motion

Created: September 03, 2021

Flashcards

What is the time period $T$ of an object in uniform circular motion?

The time taken to complete one rotation.

What are the SI units of angular velocity?
\[\text{rad}\,s^{-1}\]

How can you conceptualise angular velocity in terms of derivatives?

It’s the rate of change of angle.

What is the formula for a radian angle $\theta$ in terms of arc and radius?
\[\theta = \frac{\text{arc}}{\text{radius}}\]

What is the formula for angluar speed?
\[\omega = \frac{\theta}{t}\]

What is the formula for angular frequency?
\[\omega = 2\pi f\]

What is the formula for speed in terms of radius and angular velocity?
\[v = r\omega\]

2021-09-07

Why is no work done on an object by a centripetal force?

Because it acts at $90^\circ$ to the object’s motion.

What is the formula for centripetal acceleration $a$ in terms of velocity $v$ and angular speed $\omega$?
\[a = v\omega\]

What is the formula for centripetal acceleration $a$ in terms of radius $r$ and angular speed $\omega$?
\[a = r\omega^2\]

What is the formula for centripetal acceleration $a$ in terms of radius $r$ and velocity $v$?
\[a = \frac{v^2}{r}\]

How can you transform a formula for acceleration into one for force?

Multiply it by mass $m$.

What makes a body orbit in a circle?

The centripetal force.

In the equation for the centripetal force

\[F = mv\omega\]

which mass does $m$ represent?

The mass of the object going around in a circle.

2021-09-18

What are the three types of circular motion questions they can ask in an exam?
  • Horizontal circles
  • Vertical circles
  • Angled circles

What are the differences between horizontal circular motion and vertical circular motion?

For vertical circular motion, the force varies at the top and bottom due to gravity whereas horizontal circular motion is unaffected.

How can you work out the centripetal force from all the forces acting on an object in circular motion?

Centripetal force is the resultant force.

In vertical circular motion, why is the centripetal force larger at the top than at the bottom?

Because the normal reaction and weight are being combined.

How can you work out the speed that an object will be effectively weightless in vertical circular motion?
\[g = \frac{v^2}{r}\]

In vertical circular motion, why is the centripetal force smaller at the bottom than at the top?

Because weight is being subtracted from the normal reaction.

What is the equation for $\text{resultant force}$ at the top part of vertical circular motion?
\[\text{resultant force} = \text{weight} + \text{normal reaction}\]

What is the equation for $\text{resultant force}$ at the bottom part of vertical circular motion?
\[\text{resultant force} = \text{normal reaction} - \text{weight}\]

2021-10-01

PHOTO CONICAL MOTION Along which ‘line’ does the centripetal force act for conical motion?

$r$

PHOTO CONICAL MOTION If the centripetal force acts along the $r$ line, how could you write the force $F _ c$ in terms of $T$?
\[F_c = T\sin\theta\]

PHOTO CONICAL MOTION If the centripetal force is $T\cos\theta$, what expression could you write in terms of $T$ and $m$?
\[T\sin\theta = \frac{mv^2}{r}\]

PHOTO CONICAL MOTION Along which ‘line’ does the weight of the spinning object act for conical motion?

$h$

PHOTO CONICAL MOTION If the weight acts along the $h$ line, how could you write the force $W$ in terms of $T$?
\[W = T\cos\theta\]

PHOTO CONICAL MOTION If the weight is $T\sin\theta$, what expression could you write in terms of $T$ and $m$?
\[T\cos\theta = mg\]

PHOTO CONICAL MOTION What is the value of $\tan\theta$?
\[\frac{v^2}{rg}\]

PHOTO CONICAL MOTION What useful thing can you write to relate $\theta$ to the velocity and radius?
\[\tan \theta = \frac{v^2}{rg}\]

2022-04-12

PHOTO PLANE LIFT How does the lift force $L$ here keep the plane flying in a horizontal circle?
  • Horizontal component provides centripetal force
  • Vertical component balances out weight


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