relative angular velocity and radius of curvature questions with solutions

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• MCQmediumCircular Motionrelative angular velocity and radius of curvature

  A projectile is launched with speed U at angle θ. Find the radius of curvature when its velocity makes angle θ/2 with the horizontal.

  Options

  • Option A

    U²cos²θ/[g cos³(θ/2)]

  • Option B

    U²cos²(θ/2)/(g cosθ)

  • Option C

    U²/[g cos(θ/2)]

  • Option D

    U²cosθ/[g cos²(θ/2)]

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• NumericmediumCircular Motionrelative angular velocity and radius of curvature

  Two particles start together and move in the same direction around a circle with periods 4 s and 6 s. During the first 24 s, excluding t = 0 but including t = 24 s, if they meet N times, find N.

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• NumericmediumCircular Motionrelative angular velocity and radius of curvature

  Two particles A and B are moving in a horizontal plane anticlockwise on two different concentric circles with different constant angular velocities 2ω and ω respectively. Find the relative velocity (in m/s) of B w.r.t. A after time t = π/ω. They both start at the position as shown in figure. (Take ω = 3 rad/sec, r = 2m)

  

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• Multi-correctmediumCircular Motionrelative angular velocity and radius of curvature

  Two particles A and B move on the same circle with angular positions $\theta_{A}$ = 2t² + 3t and $\theta_{B}$= t² + 5t. Which statements are correct?

  Select all that apply

  • Option A

    $\omega_{A}$ = 4t + 3

  • Option B

    $\omega_{A}$ = 2t + 5

  • Option C

    $\omega_{AB}$ = 2t - 2

  • Option D

    At t = 1 s, their relative angular velocity is zero

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• NumericmediumCircular Motionrelative angular velocity and radius of curvature

  A particle moves along a curved path. At a certain point its speed is 6 m/s and total acceleration is 5 m/s². Its speed varies with arc length s according to v² = 16 + 6s. If the radius of curvature at that point is N m, find N.

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• MCQmediumCircular Motionrelative angular velocity and radius of curvature

  For the particle moving on the shown curved path, at point P the speed is 5 m/s and acceleration magnitude is 10 m/s², making 30° with the velocity. The rate of change of speed at P is:

  

  Options

  • Option A

    5√3 m/s²

  • Option B

    10 m/s²

  • Option C

    5 m/s²

  • Option D

    None of these

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• MCQmediumCircular Motionrelative angular velocity and radius of curvature

  For the particle moving on the shown curved path, at point P the speed is 5 m/s and acceleration magnitude is 10 m/s², making 30° with the velocity.For the same particle at point P, the radius of curvature is:

  

  Options

  • Option A

    5√3 m

  • Option B

    10 m

  • Option C

    5 m

  • Option D

    None of these

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• NumericmediumCircular Motionrelative angular velocity and radius of curvature

  A projectile is projected with speed 20 m/s at an angle 60° above the horizontal. Take g = 10 m/s². If the radius of curvature at the point of projection is N m, find N.

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• MCQeasyCircular Motionrelative angular velocity and radius of curvature

  Two moving particles P and Q are 10m apart at a certain instant. The velocity of P is 8m/s making an angle of 30° with the line joining P and Q and Q is moving with 6m/s making an angle of 30° with PQ as shown in figure. Then angular velocity of P with respect to Q is

  

  Options

  • Option A

    Zero

  • Option B

    0.1 rad/s

  • Option C

    0.4 rad/s

  • Option D

    0.7 rad/s

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• NumericmediumCircular Motionrelative angular velocity and radius of curvature

  Particles A and B move in the same direction with angular speeds 7 rad/s and 3 rad/s. Initially B is 120° ahead of A. If A first catches B after π/N seconds, find N.

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