Numerical problem on Rotational Kinetic Energy

Last updated on July 12th, 2023 at 03:56 pm

In this post, we will review the formula of Rotational Kinetic Energy and then solve Numerical problems based on Rotational Kinetic Energy.

Rotational Kinetic Energy formula from the linear kinetic energy formula

The equation for linear kinetic energy = KE_L = (1/2) m v²

Let’s Convert that equation to its angular analog:
KE = (1/2) (mr²).(v²/r²) = (1/2) (mr²).(v/r)² = (1/2) I ω²
KE_R = (1/2) I ω²

The equation of linear kinetic energy can be converted to the angular analog equation when the motion is rotational. The angular velocity ω takes the place of the linear velocity v, and the momentum of inertia (I) takes the place of the mass m.

You may wish to read a separate post specifically on the Detailed step-by-step derivation of the Rotational KE formula for class 11.

Numerical problem based on Rotational Kinetic Energy

While solving the Numericals you can have a quick look at this post: Moment of Inertia of different bodies

1 ) A 100-kg solid sphere with a radius equal to 2.0 m is rotating at 10.0 radians/s, what is its rotational kinetic energy?

Solution:

ω = 10 rad/sec

r= 2 m

m = 100 kg

For a solid sphere, the momentum of inertia I = (2/5) m r²

KE_R = (1/2) I ω² = (1/2) (2/5) m r² . ω² = (1/2) (2/5) 100 2² . 10² = 800 J

2 ) How much rotational kinetic energy does a spinning tire of mass 10.0 kg and radius 0.50 m have if it’s spinning at 40.0 rotations/s?

Solution:

ω = 40 rps = 40 x 2π rad/sec = 80π rad/sec

r= 0.5 m

m = 10 kg

For a spinning tire, the momentum of inertia I = m r²

KE_R = (1/2) I ω² = (1/2) m r² . ω² = (1/2) 10 (0.5)² . (80π)² = 78.8 x 10³ J

To revise the formulas you can have a quick look at this post: Moment of Inertia of different bodies

3 ) How much rotational kinetic energy does a spinning tire of mass 12 kg and radius 0.80 m have if it’s spinning at 200.0 radians/s?

4 )How much work do you do to spin a tire, which has a mass of 5.0 kg and a radius of 0.40 m, from 0.0 radians/s to 100.0 radians/s?

5 )How much work do you do to spin a hollow sphere, which has a mass of 10.0 kg and a radius of 0.50 m, from 0.0 radians/s to 200.0 radians/s?