Translation (linear motion) Rotation (circular motion) Quantity Formula Unit Distance s m Angle θ rad Speed 𝑣= 𝑠 𝑡 m s-1 Angular speed 𝜔= 𝜃 𝑡 rad s-1 Connection Radial distance: 𝑠=𝑟⋅𝜃 Radial speed: 𝑣=𝑟⋅𝜔

4.1 Circular motion Definitions: Period (T): time for one complete circle (revolution) Frequency (f): revolutions per second in Hertz (Hz) 𝑓= 1 𝑇 Angular displacement (θ): angle in radians (rad) Angular velocity (ω): in rad s-1 𝜔= 𝜃 𝑡 𝜔= 2𝜋 𝑇 =2𝜋𝑓 Connection between translation (linear motion) and rotation (circular motion): Radial distance: 𝑠=𝑟⋅𝜃 Radial speed: 𝑣=𝑟⋅𝜔 Centripetal force: the force that forces something to move in a circle 𝐹 𝑐 = 𝑚 𝑣 2 𝑟 𝑎 𝑐 = 𝑣 2 𝑟 (centripetal acceleration)

A record player rotates at 33 rpm. Find The angle travelled during one minute The angular speed The radial speed 20 cm from the centre The centripetal acceleration at this point

Remember: ”centripetal force” is just a generic name for any force that makes something move in a circle There is always a real force there doing the actual job (usually gravity, tension, friction or the normal force)

Ex. A fly (m = 0.0012 kg) sits 20 cm from the center of a 33 rpm record player. How big must the force of friction be so that the fly does not fall off? Ex. A hammer-throw-athlete makes 4 full revolutions of the hammer (m = 7.26 kg, r = 121 cm) in 0.86 s before letting go. How big is the average tension force in the wire?