Question

A wheel starting from rest is rotating with a constant angular acceleration of 3 rad / s². Its angular acceleration after 4 seconds will be
24 radian
14 radian
25 radian
10 radian​

Answer 1

Correct Question :

A wheel starting from rest is rotating with a constant angular acceleration of 3 rad / s². Its angular displacement after 4 seconds will be

Given :

Initial angular velocity = zero

Angular acceleration = 3 rad/s²

To Find :

Final angular velocity after 4 seconds.

Solution :

■ Angular acceleration is defined as the rate of change of angular velocity.

• It is an axial vector quantity having both magnitude as well as direction$.$
• SI unit : rad/s²
• It is a rotational analogue of linear acceleration.

❇ 2nd equation of rotational kinematics :-

• θ = ωt + 1/2 αt²

⭆ ω denotes initial angular velocity

⭆ θ denotes angular displacement

⭆ α denotes angular acceleration

⭆ t denotes time

By substituting the given values;

➠ θ = ωt + 1/2 αt²

➠ θ = (0)(4) + 1/2(3)(4)²

➠ θ = 1/2 × 3 × 16

➠ θ = 8 × 3

➠ θ = 24 radian

∴ (A) is the correct answer!