Rotational motion

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Question

Number of teeth in front and rear sprocket (tooth wheel) of a bicycle is 50 and 30 respectively. If angular speed of front sprocket is 5 radian per second then find the angular speed of the rear sprocket.

Moderate

Solution

$ω_{1} r_{1} = ω_{2} r_{2}$ ……(i)
As separation between teeth remain constant
$\frac{N_{1}}{2 π r_{1}} = \frac{N_{2}}{2 π r_{2}}$ ……(ii)
From (i) and (ii)
$\frac{ω_{1}}{ω_{2}} = \frac{N_{2}}{N_{1}} \Rightarrow ω_{1} = \frac{50}{30} \times 5 = 8.33 r a d / s$

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Column-A		Column-B (Torque of normal reaction on body B about centre of mass)
(a)	(F is directed towards\| centre of mass)	(p)	Clockwise
(b)		(q)	Anticlockwise
(c)		(r)	Zero
		(s)	Conclusion cannot be drawn with the information given