Question

the angular displacement of an object in uniform circular motion is pi/5 radian in every 0.01 sec.its frequency of revolution ​

Answer 1

GiveN :

• Angular Displacement $\sf{\theta\ =\ \dfrac{\pi }{5}\ rad}$
• Time interval = 0.01s

To FinD :

• Frequency of revolution

SolutioN :

$\implies \boxed{\boxed{\sf{\omega\ =\ \dfrac{\theta}{t}}}} \\ \\ \\ \\ \implies \sf{\omega\ =\ \dfrac{\dfrac{\pi}{5}}{0.01}} \\ \\ \\ \\ \implies \underline{\boxed{\sf{\omega\ =\ \dfrac{\pi}{0.05}\ rad s^{-1}}}}$

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Now, use formula for angular frequency :

$\implies \sf{\omega\ =\ \dfrac{2 \pi}{t}} \\ \\ \\ \\ \implies \sf{\omega\ =\ 2 \pi \nu} \\ \\ \\ \\ \implies \sf{\nu\ =\ \dfrac{\omega}{2 \pi}} \\ \\ \\ \\ \implies \sf{\nu\ =\ \dfrac{\dfrac{\pi}{0.05}}{2 \pi}} \\ \\ \\ \\ \implies \sf{\nu\ =\ \dfrac{\pi}{0.05}\ \times\ \dfrac{1}{2 \pi}} \\ \\ \\ \\ \implies \sf{\nu\ =\ \dfrac{1}{0.05\ \times\ 2}} \\ \\ \\ \\ \implies \sf{\nu\ =\ \dfrac{1}{0.1}} \\ \\ \\ \\ \implies \underline{\boxed{\sf{\nu\ =\ 10\ Hz}}}$

Answer 2

Given :

Angular displacement of an object in uniform circular motion is π/5 Radian in every 0.01 sec. so,

• Angular displacement, Δ θ = π/5 Rad
• Time taken, Δ t = 0.01 sec

To find :

• Frequency of Revolution, v = ?

Formula required :

• Formula to calculate angular velocity

     ω = Δ θ / Δ t

• Formula to calculate Frequency of revolution in terms of angular velocity

     v = ω / ( 2 π )

[ where ω is angular velocity, v is frequency, Δ θ is change in angular displacement and Δ t is change in time ]

Solution :

Calculating Angular velocity of object ( ω )

→ ω = Δ θ / Δ t

→ ω = ( π / 5 ) / 0.01

→ ω = 100 π / 5

→ ω = 20 π   Rad/sec

Calculating frequency of revolution ( v )

→ v = ω / ( 2 π )

→ v = ( 20 π ) / ( 2 π )

→ v = 10 Hertz

therefore,

• The frequency of revolution is 10 Hertz.