When disc B is brought in contact with disc A, they acquire a common angular velocity in time . The average frictional torque on one disc by the other during this period is [2007]

Question

Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia $I$ and $2 I$ respectively about the common axis. Disc A is imparted an initial angular velocity $2 ω$ using the entire potential energy of a spring compressed by a distance $x_{1}$ . Disc B is imparted an angular velocity $ω$ by a spring having the same spring constant and compressed by a distance $x_{2}$ . Both the discs rotate in the clockwise direction. [2007]

Q. When disc B is brought in contact with disc A, they acquire a common angular velocity in time $t$ . The average frictional torque on one disc by the other during this period is

Smart Achievers · Accepted Answer

(1)

When disc B is brought in contact with disc A

Let $ω$ be the common velocity. From conservation of angular momentum for the two disc system

$I (2 ω) + 2 I (ω) = (I + 2 I) ω' \Rightarrow ω' = \frac{4}{3} ω$

Torque on disc A

$τ_{A} = \frac{Δ L_{A}}{t} = \frac{L_{f} - L_{i}}{t} = \frac{I \times \frac{4}{3} ω - I \times 2 ω}{t} = \frac{- 2 I ω}{3 t}$

Here negative sign indicates that the torque creates angular retardation.

Solution

1 $\frac{2 I ω}{3 t}$

2 $\frac{9 I ω}{2 t}$

3 $\frac{9 I ω}{4 t}$

4 $\frac{3 I ω}{2 t}$

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Solution

1 2Iω3t

2 9Iω2t

3 9Iω4t

4 3Iω2t

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1 $\frac{2 I ω}{3 t}$

2 $\frac{9 I ω}{2 t}$

3 $\frac{9 I ω}{4 t}$

4 $\frac{3 I ω}{2 t}$