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As you drive down the road at 13 m/s , you press on the gas pedal and speed up with a uniform acceleration of 1.22 m/s2 for 0.55 s . You may want to review (Page 312) . Part A If the tires on your car have a radius of 33 cm, what is their angular displacement during this period of acceleration

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onyebuchinnaji

The angular displacement of the tire during the given period is 22.22 rad.

The given parameters;

  • initial velocity, u = 13 m/s
  • acceleration of the car, a = 1.22 m/s²
  • time of motion, t = 0.55 s
  • radius of the car tire, r = 33 cm = 0.33 m

The angular velocity of the car is calculated as follows;

[tex]\omega = \frac{v}{r} \\\\\omega = \frac{13}{0.33} \\\\\omega = 39.39 \ rad/s[/tex]

The angular acceleration of the car is calculated as follows;

[tex]a_r = \frac{a_c}{r} = \frac{1.22}{0.33} =3.7 \ rad/s^2[/tex]

The angular displacement of the tire is calculated as follows;

[tex]\theta = \omega t + \frac{1}{2} \alpha t^2\\\\\theta = (39.39\times 0.55) \ + \ (0.5 \times 3.7\times 0.55^2)\\\\\theta = 22.22 \ rad[/tex]

Thus, the angular displacement of the tire during the given period is 22.22 rad.

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