A top with radius 10cm, mass 2kg has a string around the edge and is initially at rest. . . .?
A top with radius 10cm, mass 2kg has a string around the edge and is initially at rest. Assume the top can be reasonably approximated as a solid cylinder. The top is held in place as the string is pulled. The string applies a force of 10N tangential to the edge for 2s.
A) What is the torque the string applies to the top?
B) What is the moment of inertia of the top?
C) What is the angular acceleration (in radians per s^2) of the top?
D) What is the angular velocity (in radians per s) of the top after 3s?
E) What is the angular momentum of the top after the string is pulled?
F) What is the kinetic energy of the top after the string is pulled?
G) After the string is pulled, the top is released. It travels away from its initial position at a linear velocity of 10 m/s. What is the rotational velocity (in radians per s) at this time? Assume no friction.
Please show your work, thank you!!
- NCSLv 76 months agoFavorite Answer
A/ torque τ = r x F = 0.10m * 10N = 1.0 N·m
B/ For a solid cylinder, moment of inertia
I = ½mr² = ½ * 2kg * (0.10m)² = 0.010 kg·m²
C/ α = τ / I = 1.0N·m / 0.010kg·m² = 100 rad/s²
D/ The angular velocity at any t ≥ 2 s is
ω = α * 2s = 200 rad/s
E/ Do you mean "after the string is done being pulled?"
angular momentum L = I*ω = 0.010kg·m² * 200rad/s = 2.0 kg·m²/s
F/ KE = ½Iω² = ½ * 0.010kg·m² * (200rad/s)² = 200 J
G/ Assuming KE is conserved, then initial KE = final KE and
200 J = ½ * 2kg * (10m/s)² + ½ * 0.010kg·m² * ω ²
ω = 141 rad/s
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