First slide

Relation between angular velocity and linear velocity

Question

Two wheels having radii in the ratio $1 : 3$ are connected by a common belt. If the smaller wheel is accelerated from rest at a rate $d f 1.5 r a d / s^{2}$ for 10 s. Find the angular velocity of bigger wheel.

Moderate

A

$15 r a d / s$
B

10 rad /s
C

5 rad /s
D

25 rad /s

Solution

$a s t h e y a r e c o n n e c t e d t h e y h a v e s a m e l i n e a r v e l o c i t y r_{1} ω_{1} = r_{2} ω_{2} ω_{2} = \frac{r_{1}}{r_{2}} ω_{1} ω_{1} = α t = 15 ω_{2} = \frac{1}{3} 15 = 5$

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