If a wheel is 4 times bigger than its original size, would the effort to rotate the (4x) larger wheel be 4 times greater than the effort to rotate the original sized wheel? i‘ve been trying to look for an answer for this question for a while and i got nothing.
TIf a wheel is 4 times bigger than its original size, would the effort to rotate the (4x) larger wheel be 4 times greater than the effort to rotate the original sized wheel? i've been trying to look for an answer for this question for a while and i got nothing. Torque makes a wheel rotate. Torque moment of inertia * angular acceleration Moment of inertia for a wheel ? * mass * radius^2 Angular acceleration Torque ÷ (? * mass * radius^2) Angular acceleration Torque ÷ (? * mass * radius^2) Torque Angular acceleration * (? * mass * radius^2) Torque Angular acceleration * ? * mass * (radius^2) So the torque needed to accelerate a wheel 4 times bigger than its original size is 16 (4^2) times bigger than the torque needed to accelerate the original wheel. If the mass is 4 times bigger, the torque is 4 times bigger I am now retired from 23 years of teaching chemistry and physics and enjoy helping people understand math, chemistry, and physics. If you would like me to answer your questions in the future, request that I be one of your contacts. Then when you post a question, I will receive it via email. Otherwise I just search randomly for a question to answer. Thanks for the opportunity to be of help
The difficulty in rotating an object depends on its moment of inertia. The inertia of an object (its mass) is a measure of how difficult it is to move an object. The moment of inertia is a measure of how difficult it is to rotate an object. The other answerer is correct about it depending on a lot of things but given that it is a wheel, I think you can safely say you are trying to rotate the wheel around it's axle. I would use a hollow cylinder to approximate the moment of inertia of a wheel since most of the mass is near the rim. The formula for the moment of inertia is I mr^2 The moment of inertia of a wheel depends on the square of the radius and depends linearly with the mass. The mass also depends on the radius. Increasing the radius by 4 times will increase the mass by 16 times since the circumference of a circle depends on the square of the radius. Replacing m with 16m and r with 4 r in the equation gives 16m (4r)^2 64 m r^2 It will be 64 times more difficult to move a wheel that is 4 times bigger. If instead of a hollow cylinder you use a solid cylinder you still get the same answer.
