Circular Motion

• What is the focus of today's revision lesson?

  Major concepts in circular motion
• What is a radian?

  A measure of an angle
• How do you convert degrees to radians?

  Multiply by $\pi$ and divide by 180
• How do you convert radians to degrees?

  Multiply by 180 and divide by $\pi$
• What is the radian equivalent of 90 degrees?

  $\frac{\pi}{2}$ radians
• What is the radian equivalent of 360 degrees?

  2$\pi$ radians
• What is the radian equivalent of 180 degrees?

  $\pi$ radians
• What is the time period in circular motion?

  Time to complete one full circle
• How is frequency related to time period?

  Frequency is one over the time period
• How do you calculate the velocity of an object in circular motion?

  Velocity = $\frac{2\pi r}{t}$
• What does angular velocity represent?

  Angular displacement per time period
• How is angular velocity calculated?

  $\omega =$$\frac{2\pi}{T}$
• How can angular velocity also be expressed in terms of frequency?

  $\omega =$$2\pi f$
• How are linear velocity and angular velocity related?

  $v =$$\omega r$
• What is the formula for centripetal force?

  $F =$$\frac{mv^2}{r}$
• What is centripetal acceleration?

  $a_c =$$\frac{v^2}{r}$
• Why can linear speed be constant while linear velocity changes in circular motion?

  Direction changes while speed remains constant
• Why does the speed of an object in circular motion not change?

  Net force is perpendicular to motion
• What is the work done by centripetal force?

  Work done is zero
• How can the centripetal force equation be rewritten using angular velocity?

  $F =$$m\omega^2 r$
• How can the centripetal acceleration equation be rewritten using angular velocity?

  $a_c =$$\omega^2 r$
• What is the procedure for investigating circular motion in an experiment?

  • Set up a mass on a string
  • Keep radius constant
  • Vary mass and measure weight
  • Time multiple oscillations
  • Calculate velocity and plot force vs. velocity squared
• What does the graph of force against velocity squared indicate?

  It should be a straight line through the origin
• How can the mass of the bond be determined from the graph?

  Gradient equals mass divided by radius
• What is the relationship between normal reaction and weight in circular motion at an angle?

  Normal reaction balances weight in vertical component
• How does the centripetal force relate to the components of normal reaction?

  Horizontal component provides centripetal force
• What is the formula for centripetal force in terms of normal reaction?

  $R \sin \theta =$$\frac{mv^2}{r}$
• What is the formula for tension in a conical pendulum?

  $T \cos \theta =$$mg$
• How is speed calculated in circular motion at an angle?

  $v =$$\sqrt{g r \tan \theta}$
• What are the forces acting in vertical circular motion?

  • Weight (mg)
  • Normal reaction (R)
  • Tension (if applicable)
• How does the normal reaction change in vertical circular motion?

  It varies depending on position
• What is the equation for normal reaction at the top of vertical circular motion?

  $R +$$mg =$$\frac{mv^2}{r}$
• What is the equation for normal reaction at the bottom of vertical circular motion?

  $R - mg =$$\frac{mv^2}{r}$
• What are the key points to remember for circular motion revision?

  • Understand radians and conversions
  • Know formulas for velocity, force, and acceleration
  • Be familiar with experiments and their setups
  • Recognize the role of forces in circular motion