Two points A and B on a disc have velocities v1 and v2, respectively, at some moment. Their directions make angles 60° and 30°, respectively, with the line of separation as shown in figure. The angular velocity of disc is:

Question

Two points A and B on a disc have velocities v1 and v2, respectively, at some moment. Their directions make angles 60° and 30°, respectively, with the line of separation as shown in figure. The angular velocity of disc is: (A) (√3 v1/d) (B) (v2/√3 d) (C) (v2-v1/d) (D) (v2/d)

Tardigrade Admin · Accepted Answer

For rigid body, separation between two points remains same.

v_{1} cos 6 0^{\circ} = v_{2} cos 3 0^{\circ}

\frac{v _{1}}{2} = \frac{3 v _{2}}{2} \Rightarrow v_{1} = 3 v_{2}

ω_{d i sc} ∣ ∣ \frac{v _{2} s i n 3 0 ^{\circ} - v _{1} s i n 6 0 ^{\circ}}{d} ∣ ∣ = ∣ ∣ \frac{\frac{v _{2}}{2} - \frac{3 v _{1}}{2}}{d} ∣ ∣

= ∣ ∣ \frac{1 v _{2} - 3 \times 3 v _{2}}{2 d} ∣ ∣ = \frac{2 v _{2}}{2 d} = \frac{v _{2}}{d} \Rightarrow ω_{d i sc} = \frac{v _{2}}{d}

Q. Two points $A$ and $B$ on a disc have velocities $v_{1}$ and $v_{2}$ , respectively, at some moment. Their directions make angles $6 0^{\circ}$ and $3 0^{\circ}$ , respectively, with the line of separation as shown in figure. The angular velocity of disc is:

$\frac{3 v _{1}}{d}$

$\frac{v _{2}}{3 d}$

$\frac{v _{2} - v _{1}}{d}$

$\frac{v _{2}}{d}$

Q. Two points A and B on a disc have velocities v1​ and v2​, respectively, at some moment. Their directions make angles 60∘ and 30∘, respectively, with the line of separation as shown in figure. The angular velocity of disc is:

d3​v1​​

3​dv2​​

dv2​−v1​​

dv2​​

Q. Two points $A$ and $B$ on a disc have velocities $v_{1}$ and $v_{2}$ , respectively, at some moment. Their directions make angles $6 0^{\circ}$ and $3 0^{\circ}$ , respectively, with the line of separation as shown in figure. The angular velocity of disc is:

$\frac{3 v _{1}}{d}$

$\frac{v _{2}}{3 d}$

$\frac{v _{2} - v _{1}}{d}$

$\frac{v _{2}}{d}$