A solid cylinder of mass 3 kg is rolling on a horizontal surface with ...
-1. The radius of the cylinder is 0.5 m. Calculate the kinetic energy of the cylinder.
First, we need to calculate the angular velocity of the cylinder, which can be found using the formula:
v = ωr
where v is the linear velocity, ω is the angular velocity, and r is the radius of the cylinder. Rearranging this formula, we get:
ω = v/r
Substituting the given values, we get:
ω = 4/0.5 = 8 rad/s
The kinetic energy of the cylinder can be calculated using the formula:
KE = (1/2)Iω^2 + (1/2)mv^2
where I is the moment of inertia of the cylinder, m is the mass of the cylinder, and v is the linear velocity.
The moment of inertia of a solid cylinder is given by:
I = (1/2)mr^2
Substituting the given values, we get:
I = (1/2)×3×(0.5)^2 = 0.375 kg m^2
Substituting all the values in the formula for KE, we get:
KE = (1/2)×0.375×8^2 + (1/2)×3×4^2
= 12 + 24
= 36 J
Therefore, the kinetic energy of the cylinder is 36 Joules.
A solid cylinder of mass 3 kg is rolling on a horizontal surface with ...