Question

A wheel has angular acceleration of 3 rad/s² and an initial angular speed of 2 rad/s. In a time of two second it has rotated through an angle (in radians) of
1. 10
2. 12
3. 4
4. 6

Answer 1

Correct Answer - Option 1 : 10

Concept:

The equations which are applied in linear motion can also be applied in angular motion.

	Linear Motion	Rotational Motion
Position	x	θ	Angular position
Velocity	v	ω	Angular velocity
Acceleration	a	α	Angular acceleration
Motion equations	x = v̅ t	θ = ω̅t	Motion equations
	v = v0 + at	ω = ω0 + αt
	\(x = {v_0}t + \frac{1}{2}a{t^2}\)	\(θ = {ω _0}t + \frac{1}{2}α {t^2}\)
	\({v^2} = v_0^2 + 2ax\)	\({ω ^2} = ω _0^2 + 2α θ\)
Mass (linear inertia)	M	I	Moment of inertia
Newton’s second law	F = ma	τ = Iα	Newton’s second law
Momentum	p = mv	L = Iω	Angular momentum
Work	Fd	τθ	Work
Kinetic energy	\(\frac{1}{2}m{v^2}\)	\(\frac{1}{2}I{ω ^2}\)	Kinetic energy
Power	Fv	τω	Power

Calculation:

Given:

α = 3 rad/s², ω_o = 2 rad/s, t = 2 s

We know that,

\(θ = {ω _0}t + \frac{1}{2}α {t^2}\)

\(θ = ({2}\times 2) + \frac{1}{2}\times3\times2^2\)

θ = 4 + 6 = 10 radians