A car has wheels of radius $0.30 m$ and is travelling at $36 m / s$ . Calculate :
(a) the angular speed of the wheel.
(b) If the wheels describe $40$ revolutions before coming to rest with a uniform acceleration.
(i) find it angular acceleration and
(ii) the distance covered.

Question

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Answer 1

Radius $r = 0.30 m$ , Velocity, $v = 36 m / s$

$(a)$ angular speed $w = \frac{v}{r} = \frac{3 6}{0 . 3} = 120 r a d / s$

$(b)$ final angular speed $w^{'} = 0$

From rotational kinematics $w^{^{'} 2} - w^{2} = 2 α θ 0 - 14400 = 2 α \times 40 \times 2 π \Rightarrow α = \frac{- 1 4 4 0 0}{1 6 0 π} = - 28.6 r a d / s^{2}$

'Distance covered

$= 40 \times 2 π r = 40 \times 2 π \times 0.3 = 75.39 m$

Answer 2

Radius $r = 0.30 m$ , Velocity, $v = 36 m / s$

$(a)$ angular speed $w = \frac{v}{r} = \frac{3 6}{0 . 3} = 120 r a d / s$

$(b)$ final angular speed $w^{'} = 0$

From rotational kinematics $w^{^{'} 2} - w^{2} = 2 α θ 0 - 14400 = 2 α \times 40 \times 2 π \Rightarrow α = \frac{- 1 4 4 0 0}{1 6 0 π} = - 28.6 r a d / s^{2}$

'Distance covered

$= 40 \times 2 π r = 40 \times 2 π \times 0.3 = 75.39 m$

A car has wheels of radius $0.30 m$ and is travelling at $36 m / s$ . Calculate :
(a) the angular speed of the wheel.
(b) If the wheels describe $40$ revolutions before coming to rest with a uniform acceleration.
(i) find it angular acceleration and
(ii) the distance covered.

The angular rim of a wheel $400$ cm in diameter has a velocity of $1600 c m s^{- 1}$ . The angular velocity of the wheel is:

The angular velocity of a wheel is $70 r a d / s$ . If the radius of the wheel is $0.5 m$ , then linear velocity of the wheel is

The angular velocity of a rickshaw wheel is $70 r a d s^{- 1}$ . If the radius of the wheel is $0.5$ m, the linear velocity is:

Wheel A has radius $10 c m$ is compled by a belt B to whell C of radius 30cm as shown in fig Wheel A increases its angular speed from rest at a uniform rate of $1.57 r a d sec^{2}$ . The time for wheel $C$ to reach a rotational speed of $100 r e v / m i n$ assuming that the belt does not slip

Revise with Concepts

Angular Velocity and its Relation With Linear Velocity

A car has wheels of radius 0.30 m and is travelling at 36 m/s. Calculate : (a) the angular speed of the wheel. (b) If the wheels describe 40 revolutions before coming to rest with a uniform acceleration. (i) find it angular acceleration and (ii) the distance covered.

Radius r=0.30m, Velocity, v=36m/s (a) angular speed w=rv​=0.336​=120rad/s (b) final angular speed w′=0 From rotational kinematics w′2−w2=2αθ0−14400=2α×40×2π⇒α=160π−14400​=−28.6rad/s2 'Distance covered =40×2πr=40×2π×0.3=75.39m

The angular rim of a wheel 400 cm in diameter has a velocity of 1600 cms–1. The angular velocity of the wheel is:

The angular velocity of a wheel is 70rad/s. If the radius of the wheel is 0.5m, then linear velocity of the wheel is

The angular velocity of a rickshaw wheel is 70 rads–1. If the radius of the wheel is 0.5 m, the linear velocity is:

Wheel A has radius 10cm is compled by a belt B to whell C of radius 30cm as shown in fig Wheel A increases its angular speed from rest at a uniform rate of 1.57radsec2 . The time for wheel C to reach a rotational speed of 100rev/min assuming that the belt does not slip

Revise with Concepts

Angular Velocity and its Relation With Linear Velocity

A car has wheels of radius $0.30 m$ and is travelling at $36 m / s$ . Calculate :
(a) the angular speed of the wheel.
(b) If the wheels describe $40$ revolutions before coming to rest with a uniform acceleration.
(i) find it angular acceleration and
(ii) the distance covered.

The angular rim of a wheel $400$ cm in diameter has a velocity of $1600 c m s^{- 1}$ . The angular velocity of the wheel is:

The angular velocity of a wheel is $70 r a d / s$ . If the radius of the wheel is $0.5 m$ , then linear velocity of the wheel is

The angular velocity of a rickshaw wheel is $70 r a d s^{- 1}$ . If the radius of the wheel is $0.5$ m, the linear velocity is:

Wheel A has radius $10 c m$ is compled by a belt B to whell C of radius 30cm as shown in fig Wheel A increases its angular speed from rest at a uniform rate of $1.57 r a d sec^{2}$ . The time for wheel $C$ to reach a rotational speed of $100 r e v / m i n$ assuming that the belt does not slip