Question: If a rolling object has a mass m and radius R, what is the expression for its rotational kinetic energy?
Options:
(1/2)Iω^2
(1/2)mv^2
(1/2)mv^2/R^2
(1/2)mv^2 + (1/2)Iω^2
Correct Answer: (1/2)Iω^2
Solution:
The rotational kinetic energy is given by (1/2)Iω^2, where I is the moment of inertia.
If a rolling object has a mass m and radius R, what is the expression for its ro
Practice Questions
Q1
If a rolling object has a mass m and radius R, what is the expression for its rotational kinetic energy?
(1/2)Iω^2
(1/2)mv^2
(1/2)mv^2/R^2
(1/2)mv^2 + (1/2)Iω^2
Questions & Step-by-Step Solutions
If a rolling object has a mass m and radius R, what is the expression for its rotational kinetic energy?
Step 1: Understand that rotational kinetic energy is the energy due to the rotation of an object.
Step 2: Know the formula for rotational kinetic energy, which is (1/2)Iω^2.
Step 3: Identify that I is the moment of inertia, which depends on the mass and shape of the object.
Step 4: For a rolling object, the moment of inertia I can be calculated using the formula I = (2/5)mR^2 for a solid sphere or I = (1/2)mR^2 for a solid cylinder.
Step 5: Substitute the moment of inertia I into the rotational kinetic energy formula to get the final expression.
Rotational Kinetic Energy – The energy possessed by a rotating object, calculated using the formula (1/2)Iω^2, where I is the moment of inertia and ω is the angular velocity.
Moment of Inertia – A measure of an object's resistance to changes in its rotation, dependent on the mass distribution relative to the axis of rotation.
Angular Velocity – The rate of rotation of an object, typically measured in radians per second.
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