Question

A torque of 100Nm,acting on a wheel of rest rotates it through 200 radians in 10 sec what is the angular acceleration?

Answer 1

Given Information

• Torque of the wheel = 100Nm
• Initial Angular Velocity = 0 rad/s
• Angular Displacement = 200 rad
• Time = 10s

We know that,

$\star \ \boxed{ \boxed{ \theta = \omega \tau + \dfrac{1}{2} \alpha { \tau} {}^{2} }}$

Substituting the values,

$\longrightarrow 200 = 0 \times 10 + \dfrac{ \alpha }{2} \times {10}^{2} \\ \\ \longrightarrow 200 = \alpha \times 10 \times 5 \\ \\ \longrightarrow 40 = \alpha \times 10 \\ \\ \longrightarrow \boxed{ \boxed{\alpha = 4 \: rad /s {}^{2} }}$

Angular acceleration of the wheel is 4rad/s².

Answer 2

Answer:

Given :-

• Torque = 100Nm
• Initial Angular Velocity = 0 rad/s
• Angular Displacement = 200 rad
• Time = 10s

To Find :-

Angular acceleration

Solution :-

$\theta = \omega \tau + \dfrac{1}{2} \alpha \times { \tau} {}^{2}$

θ= Angular Displacement

ω = Initial angular velocity

τ = Time

α = Acceleration

$\sf \:200 = 0 \times 10 + \dfrac{1}{2} \times \alpha \times {10}^{2}$

$\sf \: 200 = 0 + \dfrac{1}{2} \alpha \: \times 100$

$\sf \: 200 = 0 + 1 \alpha \: \times 50$

$\sf \: 200 = 50 \alpha$

$\alpha = \dfrac{200}{50}$

$\alpha = 4 \sf \: ms {}^{ - 1}$