Question

A disk rotates about an axis through its center. Point A is located on its rim and point B is located exactly halfway from the center toward the rim. What is the ratio of the angular velocity WA to that of @, and the tangential velocity VA to that of Vg? HINT (a) the angular velocity w, to that of ⓇA - (b) the tangential velocity VA to that of VB

Answer 1

we know that tangential velocity is the rate of change in length (arc length) (V)=

As/At

angular velocity is rate of change in angle

ادود = ا

angle   

0= Asr

where s is arc made by the point in given time by the radius r

with help of this two relations we can find that W_A/W_B=1

and V_A/V_B=2

for complete derivation as follows as

disk ASA AF where to are. center of the disk Tangential velocity (a) Angular velocity (W) we know that v= AS Angular velocity w no 48- AS Where As a where 40 - Angle made by the At = time . i radius for simplicity bet disk is rolate one comp let rotation in tine & for one complet rotation are lengtnis = 277 A = 215 [:O] in the given problem do = A Since ve are length/time. from figure as radios chages arc Valle changes but angle will not chage in given time AOA & Alls and be one 21791A - A AF = 1 ** WB 106 VB= 2018 VB = T. equal. In given time. WA= AOA AOB At