Lessee… between midnight and noon, the hour hand goes around once and the minute hand goes around twelve times. Easier than the division I was about to start with.
Don’t have to, I know exactly where my brain cramped.
Thank you; that is logic I can understand. I wish my teachers could have used this kind of approach.
I’m not refusing to accept the concept of angular velocity, I’m just refusing to accept that it’s the only way to measure the velocity of the clock’s hands for the sake of being a smartass.
If we’re being smartasses: the Earth’s speed around the sun is about 30 km/second while the hands move less than 1 m/hour around the clock face. The hands differ in speed by less than one millionth of a percent!
Same thought process here.
I chose 24 as the closest answer because the outside diameter is about twice as big as the hour hands diameter if both hands were the same length I would have chosen 12.
That’s…well, rather dubious. The length of the hands makes no difference other than to tell them apart. The hands are both attached to the clock movement. The internal mechanism of the clock is geared so that the hour hand makes 1 revolution of the clock dial in the same amount of the time the minute hand makes 12.
Yes but the tip of the hand has to travel faster because of the larger circumference at that point. Rpm does not neccessarily reflect speed. If the arm were 8,000 miles long it might be traveling close to 1,000 miles per hour.
And the hour hand would move at 83.33 mph because their movements aren’t independent of each other. They are both attached to the same mechanism that is geared to a 12:1 ratio. It doesn’t matter if it’s the alarm clock on your nightstand or if it’s Big Ben. The minute hand makes an arc of 360° in one hour and the hour hand covers 1/12 of that distance, or 30°, in the same time. That’s the clockwork governing that. In my opinion, some of you are vastly over-thinking the question. As Scotty said, “Ye cannae change the laws of physics.”
It takes 12 revolutions of the minute hand per 1 revolution of the hour hand.
I recently built a drum sander for home use. I use several different drums. If I want more speed and less torque I use a large diameter drum, if I want more torque and less speed I use a small diameter drum. They are both turning at identical rpm’s yet the larger drum has considerably more surface speed just as the minute hand on the clock has more speed at the tip than it does in the middle of its arm. Catapults are another good example.
Which have absolutely no relation to a watch or clock movement which is designed so that the ratio of the hands’ movement is 12:1. The tip of Big Ben’s minute hand may move faster than the one on a wristwatch, for example, but it still goes around the clock face 12 times in 12 hours, and the hour hand once. If the minute hand moved any faster or slower than 12x that of the hour hand, I wouldn’t trust it to keep me on schedule. Again, logic.
I agree but that doesn’t answer the question of how much faster it is moving. the hand speed is the only question asked. the hand is always at the end of the arm.
Regarding the dispute over whether to use linear velocity or angular velocity: when the problem didn’t mention the relative lengths of the minute and hour hands, I assumed angular velocity.
Or, if you’re not into the whole Occam’s Razor thing, the answer is 12r, where r is the ratio of the length of the minute hand to the length of the hour hand.
This I agree with 100%
The whole thing is usually collectively called the “hand.” I’ve never heard any part of it called an arm.
Except on the wall clock I’m looking at right now, the minute hand looks to be roughly twice the size of the hour hand. I still assert that the length of the arms is irrelevant, as both arms are attached to a movement with a 12:1 gear ratio.
What are we in disagreement about?
Read my first sentence. Since I assumed angular velocity, my answer is 12.
Had I assumed the problem wanted the difference in linear velocity, the answer for your wall clock would be (roughly) twice 12, or roughly 24.