Question

An automobile traveling at 80km/hr has tyre of radius 80cm .on applying brakes the car is brought to a stop in30 complete turns of tyres.what is the magnitude of the angular acceleration of the wheels

Answer 1

Answer on Question #66768, Physics / Mechanics | Relativity

An automobile traveling at $80\mathrm{km/hr}$ has tyre of radius 80cm. on applying brakes the car is brought to a stop in 30 complete turns of tyres. what is the magnitude of the angular acceleration of the wheels.

Solution:

The initial speed of the car

$$v = (80 \text{ km/h}) \times (1000 \text{ m/km}) \times (1 \text{ h}/3600 \text{ s}) = 22.2 \text{ m/s}.$$

The tire radius is

$$R = 0.800 / 2 = 0.4 \text{ m}.$$

So

$$\omega_0 = \frac{v}{R} = 22.2 \text{ m/s} / 0.4 \text{ m} = 55.5 \text{ rad/s}.$$

With

$$\theta = (30.0) \times (2\pi) = 188 \text{ rad} \quad \omega = 0$$ $$\omega^2 = \omega_0^2 + 2\alpha\theta$$ $$\alpha = \omega_0^2 / 2\theta = (55.5 \text{ rad/s})^2 / 2 \times 188 \text{ rad} = 8.19 \text{ rad/s}^2$$

Answer: 8.19 rad/s²

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