A wheel of radius 1 . 5 m is rotating at a constant angular acceleration of 10 rad s - 2 . Its initial angular speed is 60 π rpm . What will be its angular speed and angular displacement at t = 2 . 0 s ?

Given radius of the wheel r = 1 . 5 m , Constant angular acceleration α = 10 rad s - 2 , Initial angular speed ω i = 60 π rpm = 2 rad s - 1 . So, at time t = 2 s its angular speed ω f can be given as; ω f - ω i = α t ⇒ ω f = 10 × 2 + 2 = 22 rad s - 1 . Also, its angular displacement θ f can be given as; θ f = ω i t + 1 2 α t 2 = 2 × 2 + 1 2 × 10 × 2 2 = 24 rad . Hence, the required angular speed and angular displacement are ω f = 22 rad s - 1 and θ f = 24 radians respectively.

A wheel of radius 1 . 5 m is rotating at a constant angular acceleration of 10 rad s - 2 . Its initial angular speed is 60 π rpm . What will be its angular speed and angular displacement at t = 2 . 0 s ?

Given radius of the wheel r = 1 . 5 m , Constant angular acceleration α = 10 rad s - 2 , Initial angular speed ω i = 60 π rpm = 2 rad s - 1 . So, at time t = 2 s its angular speed ω f can be given as; ω f - ω i = α t ⇒ ω f = 10 × 2 + 2 = 22 rad s - 1 . Also, its angular displacement θ f can be given as; θ f = ω i t + 1 2 α t 2 = 2 × 2 + 1 2 × 10 × 2 2 = 24 rad . Hence, the required angular speed and angular displacement are ω f = 22 rad s - 1 and θ f = 24 radians respectively.

Calculate the following for the situation shown:- (a) Speed at D . (b) Normal reaction at D R C . (c) Height H

a From conservation of mechanical energy principle at point D with respect to point C K E C + P E C = K E D + K E D ⇒ 1 2 m v C 2 + m g R = 1 2 m v D 2 + m g 2 R ⇒ 1 2 m 7 g R 2 + m g R = 1 2 m v D 2 + 2 m g R ⇒ 7 g R + 2 g R = v D 2 + 4 g R ⇒ v D 2 = 5 g R ∴ v D = 5 g R b N + m g = m v D 2 R ⇒ N + m g = m 5 g R 2 R ⇒ N + m g = 5 m g ⇒ N = 4 m g c Energy conservation at point A and C K E A + P E A = K E C + P E C ⇒ 0 + m g H = 1 2 m v C 2 + m g R ⇒ m g H = 1 2 m 7 g R 2 + m g R ⇒ H = 7 2 R + R ∴ H = 9 2 R

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A wheel of radius $1.5 m$ is rotating at a constant angular acceleration of $10 rad s^{- 2}$ . Its initial angular speed is $(\frac{60}{π})$ $rpm$ . What will be its angular speed and angular displacement at $t = 2.0 s$ ?

Important Questions on Circular Motion

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Beta Question Bank for Medical: Physics>Chapter 7 - Circular Motion>BEGINNER'S BOX - 1>Q 11

A car has wheels of radius

0.30 m

and is travelling at

36 m s^{- 1}

. Calculate the angular speed of the wheel.

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Beta Question Bank for Medical: Physics>Chapter 7 - Circular Motion>BEGINNER'S BOX - 1>Q 12

A car has wheels of radius

0.30 m

and is travelling at

36 m s^{- 1} .

Calculate if the wheels describe

40

revolutions before coming to rest with uniform acceleration. Find its angular acceleration.

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Beta Question Bank for Medical: Physics>Chapter 7 - Circular Motion>BEGINNER'S BOX - 1>Q 13

A car has wheels of radius

0.30 m

and is travelling at

36 m s^{- 1}

. Calculate if the wheels describe

40

revolutions before coming to rest with a uniform acceleration the distance covered.

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Beta Question Bank for Medical: Physics>Chapter 7 - Circular Motion>BEGINNER'S BOX - 2>Q 1

A particle of mass

m_{1}

Is fastened to one end of a string and another one of mass

m_{2}

to the middle point; the other end of the string being fastened to a fixed point on a smooth horizontal table. The particles are then projected, so that the two portions of the string are always in the same straight line and describe horizontal circles. Find the ratio of the tensions in the two parts of the string.

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Beta Question Bank for Medical: Physics>Chapter 7 - Circular Motion>BEGINNER'S BOX - 2>Q 2

A road is

8 m

wide. Its average radius of curvature is

40 m .

The outer edge is above the lower edge by a distance of

1.28 m

. Find the velocity of vehicle for which the road is most suited?

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

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Beta Question Bank for Medical: Physics>Chapter 7 - Circular Motion>BEGINNER'S BOX - 2>Q 3

A stone of mass

1 kg

tied to a light string of length

l

= 10 m

is whirling in a circular path in the vertical plane. If the ratio of the maximum to minimum tensions in the string is

3

, find the speeds of the stone at the lowest and highest points.

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Beta Question Bank for Medical: Physics>Chapter 7 - Circular Motion>BEGINNER'S BOX - 2>Q 4

Calculate the following for the situation shown:-

Question Image
(a) Speed at $D .$
(b) Normal reaction at $D R C$ .
(c) Height $H$

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Beta Question Bank for Medical: Physics>Chapter 7 - Circular Motion>BEGINNER'S BOX - 2>Q 5

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})

A wheel of radius 1.5 m is rotating at a constant angular acceleration of 10 rad s-2. Its initial angular speed is 60π rpm. What will be its angular speed and angular displacement at t=2.0 s?

Important Questions on Circular Motion

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A wheel of radius $1.5 m$ is rotating at a constant angular acceleration of $10 rad s^{- 2}$ . Its initial angular speed is $(\frac{60}{π})$ $rpm$ . What will be its angular speed and angular displacement at $t = 2.0 s$ ?