A solid sphere of radius r = 5 cm and mass m = 0.2 kg rolls in a groove as shown.The angle,$\theta$,between the points of contact with the groove is 120 $\circ$ .If the sphere has a linear velocity of 10 mm/s,what is the rotational kinetic energy?
A)0.8 mJ
B)1.0 mJ
C)1.6 mJ
D)2.0 mJ
E)undetermined.

Question

A solid sphere of radius r = 5 cm and mass m = 0.2 kg rolls in a groove as shown.The angle,$\theta$,between the points of contact with the groove is 120 $\circ$ .If the sphere has a linear velocity of 10 mm/s,what is the rotational kinetic energy? 
A)0.8 mJ 
B)1.0 mJ 
C)1.6 mJ 
D)2.0 mJ 
E)undetermined.

Quizplus · Accepted Answer

The rotational kinetic energy of a sphere rolling without slipping is given by

KE_rotational = (2/5) * m * R^2 * w^2

where m is the mass of the sphere, R is the radius of the sphere, and w is the angular velocity of the sphere.

To find the angular velocity w, we can use the fact that the linear velocity of the sphere is related to its rotational motion by

v = R*w

where v is the linear velocity of the sphere. Plugging in the given values, we get

10 mm/s = 0.01 m/s = R*w

w = 0.01 m/s / R = 0.01 m/s / 0.05 m = 0.2 rad/s

Now we can plug in all the values to find the rotational kinetic energy:

KE_rotational = (2/5) * 0.2 kg * (0.05 m)^2 * (0.2 rad/s)^2 = 0.0016 J = 1.6 mJ

Therefore, the correct answer is choice C.

A Solid Sphere of Radius R = 5 Cm and Mass