Question

On applying a constant torque a wheel at rest turns through 400 radians in 10 sec. Find angular acceleration if same torque continues to act find angular velocity after 20 sec from start.​

Answer 1

Given

• Angular turn off the wheel = 400 rad
• Time₁ = 10 sec

To Find

• Angular acceleration
• Angular velocity if T₂ is 20 sec

Solution

● θ = ωᵢt + ½αt²

● ωբ = ωᵢ + αt

✭ Angular Acceleration :

→ θ = ωᵢt + ½αt²

• θ = Angular turn = 400 rad
• ωᵢ = Initial angular velocity = 0 rad/s
• t = Time = 10 sec

→ 400 = 50α

→ 400/50 = α

→ α = 8 rad/s²

∴ The angular acceleration is 8 rad/s²

━━━━━━━━━━━━━━━━━━━━━━━

✭ Angular Velocity :

→ ωբ = ωᵢ + αt

• ωᵢ = Initial angular velocity = 0 rad/s
• α = Angular Acceleration = 8 rad/s²
• t = Time = 20 sec

→ ωբ = 0 + 8 × 20

→ ωբ = 0 + 160

→ ωբ = 160 rad/s

∴ The angular velocity is 160 rad/s

Answer 2

Answer:

Given :-

• Angular turn off of the wheel = 400 radian
• Time taken = 10 Second

To Find :-

• Angular acceleration with same torque in 20 sec

Solution :-

Angular acceleration

$\sf \theta \: = ωᵢt + ½αt²$

$\sf \: 400 = 50 \times a$

$\sf \: 400 = 50 \: a$

$\sf \: a = \dfrac{400}{50}$

$\sf \: a = 8$

Therefore, Angular Acceleration is 8 radians/s.

Angular velocity

$\sf \: ωբ = ωᵢ + αt$

$\sf \: ωբ = 0 + 8 \times 20$

$\sf \: ωբ = 0 + 160$

$\sf \: ωբ =160 \:$

Hence

The angular velocity is 160 rad/s.