Question

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Answer 1

Question :

A wheel has a constant angular acceleration of 2 rad/s², During a certain 4s interval, it turns through an angle of 72 rad. Assuming that at t = 0, angular speed ω⁰ = 6 rad/s how long, is motion at the start of this 4 s interval?

A) 7 sec

B) 9 sec

C) 4 sec

D) 10 sec

Answer :

★ First case :

• α = 2 rad/s²
• t = 4s
• θ = 72 rad

First we need to find initial angular velocity of wheel$.$

Using second equation of rotational kinematics,

➝ θ = ωt + 1/2 αt²

➝ 72 = 4ω + 1/2 (2)(4)²

➝ 72 = 4ω + 16

➝ 4ω = 56

➝ ω = 14 rad/s

★ Second case :

• ω⁰ = 6 rad/s
• ω = 14 rad/s
• α = 2 rad/s²

In this case we have asked to find time.

Using first equation of rotational kinematics,

➝ ω = ω⁰ + αt

➝ 14 = 6 + 2t

➝ 8 = 2t

➝ t = 4 s

∴ (C) is the correct answer!