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31 March, 18:31

A race car driver is driving his car at a constant speed of 45.0 m/s on a circular track with a radius of 285 m. (a) What is the angular speed (in rad/s) of the car? rad/s (b) What are the magnitude (in m/s2) and direction of the car's acceleration? magnitude m/s2 direction

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  1. 31 March, 20:10
    0
    (a) 0.158 rad/s.

    (b) 7.1 m/s² toward the center of the circular track.

    Explanation:

    (a)

    Using,

    v = ωr ... Equation 1

    Where v = speed of the car, r = radius of the circular track. ω = angular speed.

    make ω the subject of the equation

    ω = v/r ... Equation 2

    Given: v = 45 m/s, r = 285 m.

    substitute into equation 2

    ω = 45/285

    ω = 0.158 rad/s

    Hence the magnitude of the angular speed of the car = 0.158 rad/s.

    (b)

    Using

    a = v²/r ... Equation 3

    Where a = acceleration of the car

    Given: v = 45 m/s, r = 285 m

    Substitute into equation 3

    a = 45²/285

    a = 2025/285

    a = 7.1 m/s² toward the center of the circular track.
  2. 31 March, 21:10
    0
    A) Angular velocity = 0.1579 rad/s

    B) Acceleration = 7.11 m/s² in a direction towards the centre of the circle motion

    Explanation:

    In circular motion,

    linear speed = angular speed x radius of the rotation

    Thus,

    v = ωr

    Where;

    v = linear speed (m/s)

    ω = angular speed (radians/s)

    r = radius of the rotation (m)

    We are looking for angular speed, thus; making ω the subject, we have;

    ω = v/r

    We are given that v = 45 m/s and r = 285m

    Thus,

    ω = 45/285 = 0.1579 rad/s

    B) The formula for Centripetal acceleration is given as;

    a_c is given by the expression

    a_c = rω² = v²/r

    where;

    v is linear velocity of the object,

    ω is its angular velocity and

    r is the radius of the circle in which object moves.

    Thus,

    a_c = v²/r = 45²/285 = 7.11 m/s²

    The centripetal acceleration affects the direction of the car. So in this case the direction of the car will be towards the centre of the circle motion.
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