Question

An automobile moves on a road with a speed of 54 km h⁻¹. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m². If the vehicle is brought to rest in l 5s, the magnitude of average torque transmitted by its brakes to the wheel is:

Options

• 8.58 kg m² s⁻²

• 10.86  kg m² s⁻²

• 2.86  kg m² s⁻²

• 6.66  kg m² s⁻²

Answer 1

6.66  kg m² s⁻²

Explanation:

Given: speed V = 54 kmh⁻¹ = 15 ms⁻¹ 

Moment of inertia, I= 3 kgm² 

Time t= 15s

ω_i = `"V"/"r" = 15/0.45 = 100/3 ω_"f" = 0`

ω_f = ω_i + αt

0 = `100/3 + (-α) (15)`

⇒ α = `100/45`

Brakes' average torque delivered to the wheel

τ = (I)(α) = `3 xx 100/45`

= 6.66  kg m² s⁻²