Question

A disc of mass 100 g is rolling without slipping on a horizontal surface with a velocity of 10 cm s^(-1). Calculate its total energy.

Answer 1

Answer:

Total K.E=3/4mv^2(Translational K.E.+Rotational K.E.)

              =3/4*.1*0.01

               =0.00075 J

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Answer 2

Given:

Mass of the disc = 100g

Velocity of the disc = 10 cm/sec

To find:

Total Kinetic energy of the disc.

Solution:

The total kinetic energy of a body is the sum of kinetic energies due to all forms of motion.

In this case, the disc is rolling, therefore there will be translational kinetic energy and rotational kinetic energy.

mass of disc = 100 g = 0.1 kg

angular velocity = V/r

V = 10 cm/sec = 0.1 m/sec

The rotational kinetic energy of the disc:

K.E. 1 = $\frac{3}{4}$ x mass x $(radius)^2$ x $(Angular velocity)^2$

putting the values we get

K.E. 1 =  $\frac{3}{4}$ x mass x $(velocity)^2$

K.E. 1 = 0.00075 joules.

Similarly,

The translational kinetic energy of the disc

K.E. 2 = $\frac{1}{2}$ x mass x $(velocity)^2$  

K.E. 2 = 0.0005 joules

Total kinetic energy = K.E. 1 + K.E. 2

Total kinetic energy = 0.00075 + 0.0005

Total kinetic energy = 0.00125 Joules

Therefore, the total kinetic energy of the disc will be 0.00125 joules.