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Grade 11Mechanics

An automobile on a road moves with a speed of 54km/h.The radius of its wheels is 0.35m.What is the average torque transmitted by its brakes to a wheel,if the vehicle is brought to rest in 15s?The moment of inertia of the wheel about its axis of rotation is 3kgm2.

Apu

7 Years agoGrade 11

1 Answer

Arun

7 Years ago

Hello Dear.

Given Conditions ⇒

Initial linear velocity(u) = 54 km/hr.
= 54 × 5/18 [Changing into m/s.]
= 15 m/s.
Radius of the wheel(r) = 0.35 m.

Now, Using the Formula,

Initial Angular Velocity (ω₁) = u/r
ω₁ = 15/0.35
ω₁ = 42.86 radian/sec.

Also, Final Angular Velocity (ω₂) = 0

Now, Using the Formula,
Angular Acceleration (α) = (ω₂ - ω₁)/t
= (0 - 42.86)/15
= - 2.86 radian/sec²

Moment of Inertia about the axis of the rotation(I) = 3 kg-m²

∴ Torque = I × α
⇒ Torque = 3 × -2.86
⇒ Torque = -8.58 Nm.

Hence, the average negative torque is -8.58 N-m.

Regards
Arun (askIITiams forum expert)

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