Question

In the figure, wheel A of radius 13 cm is coupled by belt B to wheel C of radius 23 cm. Wheel A increases its angular speed from rest at a uniform rate of 1.7 rad/s2. Find the time for wheel C to reach a rotational speed of 300 rpm, assuming the belt does not slip. (Hint: If the belt does not slip, the linear speeds at the rims of the two wheels must be equal.)

Answer 1

radius of wheel A is rA = 8 cm
radius of wheel B is rB = 23 cm
Angular acceleration of the wheel α = 1.7 rad/s2
Angular speed of the wheel C is ωc = 300 rpm = 31.42 rad/s
Because both wheels are connected with same belt so they

have same tanegntial speed then tangential acceleration
aA = aB
rAαA= rBαB
So, the angular acceleration
αB = rAαA / rB = [(13 cm) / (23 cm)](1.7 rad/s2 ) = 0.96 rad/s2
Since angular speed of wheel C is ω = 31.42 rad/s

Hence, the time is,

t = ω/α = 31.42 rad/s / 0.96 rad/s2 = 32.7 s