A rolling object has a radius R and rolls with a speed v. What is its total kinetic energy?
Practice Questions
1 question
Q1
A rolling object has a radius R and rolls with a speed v. What is its total kinetic energy?
(1/2)mv^2
(1/2)mv^2 + (1/2)Iω^2
(1/2)mv^2 + (1/2)mv^2
(1/2)mv^2 + (1/2)mv^2/R^2
The total kinetic energy is the sum of translational and rotational kinetic energy: (1/2)mv^2 + (1/2)Iω^2.
Questions & Step-by-step Solutions
1 item
Q
Q: A rolling object has a radius R and rolls with a speed v. What is its total kinetic energy?
Solution: The total kinetic energy is the sum of translational and rotational kinetic energy: (1/2)mv^2 + (1/2)Iω^2.
Steps: 5
Step 1: Understand that a rolling object has two types of motion: it moves forward (translational) and it spins (rotational).
Step 2: The formula for translational kinetic energy (the energy due to forward motion) is (1/2)mv^2, where m is the mass and v is the speed.
Step 3: The formula for rotational kinetic energy (the energy due to spinning) is (1/2)Iω^2, where I is the moment of inertia and ω is the angular velocity.
Step 4: To find the total kinetic energy of the rolling object, you need to add the translational and rotational kinetic energy together.
Step 5: The final formula for total kinetic energy is: Total KE = (1/2)mv^2 + (1/2)Iω^2.
