Two particles A and B move anticlockwise with the same speed v in a circle of radius R and are diametrically opposite to each other.At t = 0 , A is given a constant acceleration (tangential) a t = 72 v 2 25 πR . calculate the time in which A collides with B , The angle traced by A ,its angular velocity and radial acceleration at the time of collision.

According to rotational equation of motion, θ = ω t + 1 2 g t 2 π R = 1 2 × 72 v 2 25 π R × t 2 ⇒ t = 5 πR 6 v Using displacement-time equation s = u t + 1 2 g t 2 R θ = u 5 π R 6 v + 1 2 × 72 v 2 25 πR × 25 π 2 R 2 36 v 2 ⇒ θ = 5 π 6 + π = 11 π 6 a T = 72 v 2 25 πR R θ = v 5 πR 6 v + πR = 11 6 π Angular velocity is given by ω = ω v + α t ω = v R + 72 v 2 25 πR 2 × 5 πR 6 v ω = v R + 12 v 5 R ω = 17 v 5 R Angular acceleration α = ω 2 R = 289 v 2 25 R

Starting from rest, a particle rotates in a circle of radius R = 2 m with an angular acceleration α = π 4 rad sec 2 . Calculate the magnitude of average velocity of the particle over the time it rotates quarter circle.

Given, Radius of circular path is, R = 2 m Angular acceleration of particle is, α = π 4 rad s - 2 Initial angular velocity is, ω 0 = 0 Angle turned in quarter circle is, θ = π 2 rad Using second equation of motion for circular motion, θ = ω 0 t + 1 2 α t 2 ⇒ π 2 = 0 + 1 2 α t 2 ⇒ π 2 = 1 2 × π 4 × t 2 ⇒ t 2 = 4 ⇒ t = 2 s Average velocity is given by, v a v g = Total displacement Total time v a v g = R 2 + R 2 t ⇒ v a v g = R 2 2 = 2 2 2 = 1 m s - 1 ∴ Average velocity = 2 R t = 1 ms − 1

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Two particles $A$ and $B$ start at $O$ and travel in opposite direction along the circular path at constant speed $v_{A} = 0.7 {ms}^{- 1}$ and $v_{A} = 1.5 {ms}^{- 1}$ respectively. Determine the when they collide and the magnitude of the acceleration of $B$ just before this happening.(radius= $5 m$ )

Important Questions on Circular Motion

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Beta Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise-4>Q 2

A particle is moving in a circular orbit with a constant tangential acceleration. After a certain time

t

has elapsed after the beginning of motion, the angle between the total acceleration a and the direction along the radius

r

becomes equal to

45 ° .

What is the angular acceleration of the particle.

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Beta Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise-4>Q 3

Two particles

A

and

B

move anticlockwise with the same speed

v

in a circle of radius

R

and are diametrically opposite to each other.At

t = 0, A

is given a constant acceleration (tangential)

a_{t} = \frac{72 v^{2}}{25 πR} .

calculate the time in which

A

collides with

B

, The angle traced by

A

,its angular velocity and radial acceleration at the time of collision.

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Beta Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise-4>Q 4

A square plate is firmly attached to a frictionless horizontal plane. One end of a taut cord is attached to point $A$ of the plate and he cord gets wrapped around the plate. The sphere is given an initial velocity $v_{0}$ on the horizontal plane perpendicular to the cord which causes it to make a complete circle of the plate and return to point $A$ . Find the velocity of the sphere when it hits point $A$ again after moving in a circle on the horizontal plane. Also find the time taken by the sphere to complete the circle.

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Beta Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise-4>Q 5

Starting from rest, a particle rotates in a circle of radius

R = \sqrt{2} m

with an angular acceleration

α = \frac{π}{4} rad \sec^{2}

. Calculate the magnitude of average velocity of the particle over the time it rotates quarter circle.

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Beta Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise-4>Q 6

A stone weighing

0.5 kg

tied to a rope of length

0.5 m

revolves along a circular path in a vertical plane. The tension of the rope at the bottom point of the circle is

45 N

. To what height will the stone rise if the rope breaks at the moment when the velocity is directed upwards?

(g = 10 m s^{- 2})

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Beta Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise-4>Q 7

A hemisphere of radius $R$ and of mass $4 m$ is free to slide with its base on a smooth horizontal table. A particle of mass $m$ is placed on the top of the hemisphere. Find the angular velocity of the particle relative to hemisphere an angular displacement $θ$ when velocity of hemisphere has become $v$ .

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Two particles A and B start at O and travel in opposite direction along the circular path at constant speed vA=0.7ms-1 andvA=1.5ms-1 respectively. Determine the when they collide and the magnitude of the acceleration of B just before this happening.(radius=5m)

Important Questions on Circular Motion

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