Apulley of radius r has a string wrapped around it. a force is applied to the free end of the string such that the string has a tension t. assume that the pulley is rotating with constant angular velocity in the counter-clockwise direction (this could be accomplished by a frictional force which is counteracting the torque due to the string). convince yourself that while the pulley rotates by an angle θ a point on the boundary of the pulley moves by the distance d=rθ. therefore the work done by the tension force on the pulley is given by w=td=trθ.

a. what is the torque τ on the pulley due to the tension in the rope?

b. rewrite the expression for the work done on the pulley by the rope (given above) using your expression for the torque τ. the formula you obtain is the general formula for the work done by a torque on a rotating object. explain why it can be said that this formula is analogous to the formula for work done by a force for linear motion.

note: the given question is incomplete.

complete question is given below.

which is an example of kinetic energy?

a. the energy stored in ethanol  

b. a hockey puck sliding across the ice  

c. a compressed spring  

d. a ball sitting at the top of a ramp

solution: the kinetic energy is the energy posses by the virtue of the motion of the object.

in the given options, a, c and d are the example of potential energy because it is the energy posses by the virtue of the rest of the object. but option b has the kinetic energy as the object is in motion.

hence, a hockey puck sliding across the ice   is the apex example of kinetic energy.

so, the option (b) a hockey puck sliding across the ice   is the correct option.

bacteria that live on the ocean floor are sustained by phytoplankton. phytoplankton, microscopic marine photosynthetic organisms, have a vastly significant role to play not only in the marine food web of which they’re part of, but also on a more global scale. despite their infinitely small size in comparison to other marine organisms, these tiny creatures occupy an immensely important ecological niche: they are the foundation of the marine food web, and as primary producers, play key roles in supporting all other organisms in the marine environment, as well as in the regulation of the earth’s climate through the sequestration of carbon, oxygen production, and other related processes. phytoplankton account for roughly half of all global primary productivity; therefore, their significance extends far beyond the marine environment alone. there is an intriguing sense of irony in the realization that these tiny living beings that often live out their existence unnoticed and undetected by the rest of the world, have such a far-reaching impact on the lives of virtually all other living organisms on the planet, particularly on those in the marine environment. the world that we have become accustomed to has been and is continuously shaped by the workings of these miniscule yet vital “plants of the sea”.

hope this !

magnets not strong enough

explanation: