Question

A child rolls a 4.984g nickel across the floor. The nickel has a radius of 1.05 cm.
a) Calculate it's Moment of Inertia in SI units.

b) If the above nickel had a torque of 2.56 x 10^-4 Nm during the beginning of the roll, compute the angular acceleration of the nickel.

Answer 1

(a) Given the mass of the nickel (five-cent coin) is M = 4.984g = 4.984 x 10-3kg and the radius of the nickel is R = 1.05cm = 1.05 x 10-2m. The coin can be assumed as a solid disc. The moment of inertia of a solid disc about an axis passing through the centre of mass and perpendicular to its plane is

So the moment of inertia of the nickel is 2.75 x 10-7 kgm2.

(b) The torque of the nickel is given as = 2.56 x10-4 Nm. If was the angular acceleration of the nickel, then the torque is given by,

So the angular acceleration of the nickel was 930.91 rad/s2.