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System of Particles and Rotational Motion

Angular displacement, angular velocity, angular acceleration

A particle moves uniformly in a circle with a time period of 0

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Solving time: 3 mins

A particle moves uniformly in a circle with a time period of $0.314 s$ . At time $t = 0$ the particle is on the $x$ -axis at $A$ (see figure) and is moving anticlockwise. Radius of the circle is $1.0 m$ . Write velocity of the particle at time $t = 3.17925 s$ using unit vector $\hat{i}$ and $\hat{j}$ .

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Physics for JEE Main and Advanced Mechanics 1 (McGraw Hill)

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A particle moves uniformly in a circle with a time period of

0.314 s

. At time

t = 0

the particle is on the

x

-axis at

A

(see figure) and is moving anticlockwise. Radius of the circle is

1.0 m

. Write velocity of the particle at time

t = 3.17925 s

using unit vector

\hat{i}

and

\hat{j}

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

Speed

v = ω r = \frac{2 π}{T} \cdot r = \frac{2 \times 3.14}{0.314} \times 1 = 20 ms^{- 1}

Velocity vector at this instant is

v = v \hat{θ}

and

\hat{θ} = (- sin \frac{π}{4}) \hat{i} + (cos \frac{π}{4}) \hat{j}

v = - \frac{1}{2} \hat{i} + \frac{1}{2} \hat{j} = 20 (- \frac{1}{2} \hat{i} + \frac{1}{2} \hat{j}) = (- 102 \hat{i} + 102 \hat{j}) ms^{- 1}

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Question Text	A particle moves uniformly in a circle with a time period of $0.314 s$ . At time $t = 0$ the particle is on the $x$ -axis at $A$ (see figure) and is moving anticlockwise. Radius of the circle is $1.0 m$ . Write velocity of the particle at time $t = 3.17925 s$ using unit vector $\hat{i}$ and $\hat{j}$ .
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	144

Text solutionVerified

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A particle moves uniformly in a circle with a time period of 0.314 s. At time t=0 the particle is on the x-axis at A (see figure) and is moving anticlockwise. Radius of the circle is 1.0 m. Write velocity of the particle at time t=3.17925 s using unit vector i^ and j^​.

Text solutionVerified

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