Question

Physics I Pre-Lab Assignment: Rotational Kinetic Energy On a blank piece of paper (lined or computer, nothing torn out of a notebook), please answer the questions below. The assignment is due before lab starts. 1. When an object rolls down an incline, its kinetic energy is composed of both rotational and translational terms. Write out the equation for total kinetic energy with rotational and translational components. Label the terms to identity which is rotational and which is translational. 2. A uniform ball of mass 7 kg and radius R rolls smoothly from rest down a ramp at angle 8 = 30'. If the ball descends a vertical height of 1.2 m, what is its speed at the bottom?

Answer 1

1. Let's say the object descends hight "h" so using conservation of mechanical energy.

Total KE = (1/2)Mv² + (1/2)Iω² = Mgh

Translational Kinetic Energy =  (1/2)Mv²

Rotational Kinetic Energy =  (1/2)Iω²

Where M = Mass of the object

v = Velocity of it's com

I = Moment of inertia about COM

ω = Angular Velocity

2. Using conservation of mechanical energy

(1/2)Mv² + (1/2)Iω² = Mgh

(1/2)Mv² + (1/2)(2MR²/5)ω²​​​​​​​ = Mgh

For Pure rolling v = Rω

(1/2)Mv² + (1/5)Mv² = Mgh

(7/10)v² = gh

v² = (10/7)gh

v = √(10gh/7)

v = √(120/7)

v = 4.14 m/s