Question

a rigid body rotates about a fixed axis with variable angular speed (in rad /s) w=3-5t at any time t (in second) . the angle through which it rotates before it comes to rest is​

Answer 1

Answer

• Angle of rotation before coming to rest = 0.9 Rad

Explanation

Given:-

• A rigid body rotates about a fixed axis with a variable angular speed (in rad/sec) at any time 't' (in seconds)
• angular speed, ω = 3 - 5t  rad/sec

To find:-

• The angle through which it rotates before coming to rest, θ =?

Formula required:-

• The Formula for instantaneous angular velocity

        ω = d(θ) / d(t)

[Where ω is angular acceleration, θ is angular displacement, t is the time]

Solution:-

As given,

we need to find the angle of rotation just before the body comes to rest.

so, at that time angular velocity (ω) will be zero.

→ ω = 0

→ 3 - 5t = 0

→ -5t = -3

→ t = 3/5  sec

Now, Using the formula for instantaneous angular acceleration

→ ω = d(θ) / d(t)

→ d(θ) = ω d(t)

[Integrating both sides]

→ ∫ d(θ) = ∫ [ω d(t)]

→ θ = ∫[(3 - 5t) d(t)]

→ θ = 3t - (5t²/2)

[Now, putting t = 3/5]

→ θ = 3×3/5 - [5(3/5)²/2]

→ θ = 9/5 - 9/10

→ θ = 9/10 = 0.9 rad

Therefore,

• The Angle at which body rotates before coming to rest is 0.9 Radians.    

Answer 2

Explanation:

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