Period and Frequency Recall that 1 revolution 2 radians frequency(f)=revolutions /second angular velocity (o)= radians /second(b) By combining(a) and(b) =2πf R Realize that: S period (D=seconds/revolution So T=1/f= 2/o =2x/T=2f Physics 121: Lecture 10, Pg 11
Physics 121: Lecture 10, Pg 11 Period and Frequency Recall that 1 revolution = 2 radians frequency (f ) = revolutions / second (a) angular velocity () = radians / second (b) By combining (a) and (b) = 2 f Realize that: period (T) = seconds / revolution So T = 1 / f = 2/ R v s = 2 / T = 2f v R s
Recap: X=R COS(0)=R coS(ot) y=R sin(0)=R sin(ot) 0= tan1 (y/x) R S 0= ot =0t s=vt S=R0 Rot V=OR Physics 121: Lecture 10, Pg 12
Physics 121: Lecture 10, Pg 12 Recap: R v s =t (x,y) x = R cos() = R cos(t) y = R sin() = R sin(t) = tan-1 (y/x) = t s = v t s = R = Rt v = R
Acceleration in UCM Even though the speed is constant, velocity is not constant since the direction is changing must be some acceleration Consider average acceleration in time△t>an=△v/△t △v R Physics 121: Lecture 10, Pg 13
Physics 121: Lecture 10, Pg 13 Acceleration in UCM: Even though the speed is constant, velocity is not constant since the direction is changing: must be some acceleration ! Consider average acceleration in time t v2 R v1 v v1 v2 aav = v / t
Acceleration in UCM Even though the speed is constant, velocity is not constant since the direction is changing Consider average acceleration in time At y av=v/At R △v seems like△v( hence△w△t) points toward the origin Physics 121: Lecture 10, Pg 14
Physics 121: Lecture 10, Pg 14 Acceleration in UCM: seems like v (hence v/t ) points toward the origin ! R Even though the speed is constant, velocity is not constant since the direction is changing. Consider average acceleration in time t aav = v / t v
Acceleration in UCM Even though the speed is constant, velocity is not constant since the direction is changing As we shrink△t,△v/Atc>a/t=a Ra=dv/dt We see that a points in the -r direction Physics 121: Lecture 10, Pg 15
Physics 121: Lecture 10, Pg 15 Acceleration in UCM: Even though the speed is constant, velocity is not constant since the direction is changing. As we shrink t, v / t dv / dt = a a = dv / dt We see that a points in the - R direction. R