How to Calculate the Speed and Rotational Kinetic Energy of a Rotating Disk
Question:
Starting from rest, you pull a string wrapped around a disk of mass m = 1.6 kg and radius R = 0.11 m with a constant force F = 8 N along a nearly frictionless surface. At the instant when the center of the disk has moved a distance x = 0.11 m, your hand has moved a distance of d= 0.33 m.
(a) What is the speed of the center of mass of the disk at this instant?
(b) How much rotational kinetic energy does the disk have relative to its center of mass?
Answer:
To find the speed of the center of mass of the disk, we can use the equation Vcom = dcom/t, where dcom is the distance the center of the disk has moved and t is the time taken. Additionally, the rotational kinetic energy of the disk can be found using the formula Krot = (1/2)Iω2.
Explanation:
To find the speed of the center of mass of the disk, we can use the equation: Vcom = dcom/t. In this case, dcom = 0.11 m and t can be calculated using the formula: t = d/v. Where d is the distance your hand has moved and v is the speed of your hand.
In this case, d = 0.33 m and v can be calculated using the formula: v = F/m. Plugging in the given values, we can find the speed of the center of mass of the disk.
Additionally, the rotational kinetic energy of the disk can be found using the formula: Krot = (1/2)Iω2. Where I is the moment of inertia of the disk and ω is the angular velocity. Plugging in the given values, we can find the rotational kinetic energy of the disk relative to its center of mass.