Question

A car with 80 cm diameter wheel starts from rest and accelerates uniformly to a velocity of 20 m/s in 9.0s. Find the angular acceleration in rad/s2.

Answer 1

Answer on Question55211 - Physics / Mechanics — Kinematics — Dynamics - for completion

October 1, 2015

A car with $D = 80\, \text{cm}$ diameter wheel starts from rest and accelerates uniformly to a velocity of $v_1 = 20\, \text{m/s}$ in $t_1 = 9.0\, \text{s}$. Find the angular acceleration in $rad/s^2$.

Solution

The angular velocity of the wheel after the acceleration is:

$$\omega_1 = \frac{v_1}{R} = \frac{2v_1}{D}$$

where $R$ is the radius of the wheel.

The angular acceleration:

$$\varepsilon = \frac{\omega_1}{t_1} = \frac{2v_1}{Dt_1} = \frac{2 \cdot 20\, \text{m/s}}{0.8\, \text{m} \cdot 9\, \text{s}} \approx 5.6\, \text{rad/s}^2$$

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