Circular Motion

Radians

Angle at the centre of a circle subtended by an arc which is equal in length to the radius of the circle is 1 radian.

  • Angle⠀in⠀Radians=Arc⠀Length⁡RadiusAngle⠀in⠀Radians=\frac{Arc⠀Leng\operatorname{th}}{Radius}

  • θ=sr\theta=\frac{s}{r}

  • Degrees=Radians⋅180πDegrees=Radians\cdot\frac{180}{\pi}

  • Radians=Degrees⋅π180Radians=Degrees\cdot\frac{\pi}{180}

Angular Velocity

Rate of change of an angle with respect to time.

ω=θt\omega=\frac{\theta}{t}

SI Unit: radian per second (rad s-1)

  • Scalar quantity

The greater the distance a particle on the disc is from the centre, the greater its linear velocity.

v=rwv=rw

Centripetal Force

The force needed to keep a body moving in a circle.

  • F=mv2rF=\frac{mv^2}{r}

  • F=mw2rF=mw^2r

Centripetal Acceleration

The acceleration of a body towards the centre when it is moving in a circle.

Period

Time taken for a body to make one full rotation.

T=2πrvT=\frac{2\pi r}{v}

Satellite Orbit

T2=4π2r3GMT^2=\frac{4\pi^2r^3}{GM}