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Converting Between Linear & Rotational quiz

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  • What equation connects linear displacement (Δx) and angular displacement (Δθ) in rotational motion?
    Δx = r * Δθ, where r is the radius of rotation.
  • How do you calculate tangential velocity (Vt) from angular velocity (ω)?
    Vt = r * ω, with r being the radial distance from the center.
  • What is the formula for tangential acceleration (At) in terms of angular acceleration (α)?
    At = r * α, where r is the radius and α is angular acceleration.
  • Do the equations Vt = r * ω and At = r * α apply to centripetal acceleration?
    No, these equations apply only to tangential acceleration, not centripetal acceleration.
  • What are the three types of acceleration discussed in rotational motion?
    Tangential acceleration (At), centripetal acceleration (Ac), and angular acceleration (α).
  • How do rotational quantities like Δθ, ω, and α behave across a rigid rotating body?
    They are the same at every point on the rigid rotating body.
  • Why do linear speeds differ at various points on a rotating disk?
    Linear speed depends on the radial distance (r) from the center; points farther out move faster.
  • If a wheel spins at 10 radians per second, what is the angular velocity at the center, halfway, and edge?
    The angular velocity (ω) is 10 radians per second at all points.
  • How do you calculate the tangential velocity at a point 4 meters from the center of a wheel spinning at 10 rad/s?
    Vt = r * ω = 4 m * 10 rad/s = 40 m/s.
  • What is the tangential velocity at the edge (8 meters from center) of a wheel spinning at 10 rad/s?
    Vt = r * ω = 8 m * 10 rad/s = 80 m/s.
  • What is the tangential velocity at the exact center of a spinning wheel?
    It is zero, because the radial distance r is zero.
  • What happens to your linear velocity if you are at the edge of a spinning carousel compared to the center?
    You move faster at the edge because your radial distance from the center is greater.
  • If you are spinning in place at the center of a rotating disk, what type of motion do you experience?
    You experience angular velocity (ω) but no linear velocity (Vt).
  • What is the relationship between linear and rotational variables in the conversion equations?
    Linear variables are multiplied by the radius to convert to their rotational equivalents.
  • Why do all points on a rotating disk share the same angular velocity but not the same linear velocity?
    Angular velocity is uniform for the whole disk, but linear velocity depends on each point's distance from the center.