Question

The angular speed of a motor wheel is increased from 1200 rpm to 3120 rpm in 16sec.? find.
(A) Angular acceleration
(B) Assuming acceleration to be uniform, how many rotations does the engine make on this bike?
(C) State law of conservation of linear momentum?

Answer 1

Hint
Angular speed is the measure of how fast the central angle of a rotating body changes with respect to time. In this short piece of article, let us learn more angular speed formula, the relationship between angular speed and linear speed along with a few angular speed problems.

Complete step by step answer
According to the question initial angular speed is 1200 rpm
Let initial angular speed is, $ {\omega _1} = 1200rpm = \dfrac{{1200 \times 2\pi }}{{60}} = 40\pi $ red.s-1 [converting rpm into rad/s]
Same as, final angular speed is $ {\omega _2} = 3120rpm = \dfrac{{3120 \times 2\pi }}{{60}} = 104\pi $ red.s-1
And, the time difference ∆t = 16 sec
(1)angular acceleration,according to the formula
 $ a = \dfrac{{({\omega _2} - {\omega _1})}}{{\Delta t}} $
Put the known values in the equation,
 $ \Rightarrow a = \dfrac{{104\pi - 40\pi }}{{16}} = 4\pi $ red/s.
(2)angle, $ \theta = {\omega _1}\Delta t + \dfrac{1}{2}a\Delta {t^2} $
 $ \Rightarrow \theta = 40\pi 16 + \dfrac{1}{2}(4\pi ) \times 256 $
$∴ θ = 1152 rad$.
(3) When there is no external force applied on a system of partials then momentum of the system of particles will be consecrated or you can say that if external force is zero, then momentum of the system of particles is initially = Momentum of the system of particles is finally.

Note
The angular momentum is a vector quantity that is a measure of the rotational momentum of a rotating body or system, that is equal in classical physics to the product of the angular velocity of the body or system and its moment of inertia with respect to the rotation axis, and that is directed along the rotation axis.