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Classical Mechanics Level 2

Two clocks $A$ and $B$ of radii $r$ and $R$ respectively, with $r<R$ , show the same time.

The tip of the minute hand of which clock will move with greater speed ?

Both will move with the same speed

B

A

They will not move at all

5 solutions

Sravanth C.
Feb 17, 2015

The radius of the clock B is bigger, so it has to travel longer distance. the radius of the clock A is smaller. therefore the minute hand of clock B should travel with greater speed to match the correct time.

But when we measure the velocity for circular motion, we usually consider the angular velocity. And shouldn't the angular velocity be the same for both the clocks?

Prasun Biswas - 6 years, 3 months ago

I too thought the same way..:(

Anandhu Raj - 6 years, 3 months ago

Angular velocity is same but not the linear speed. Linear speed is more for clock B (bigger than A) as linear velocity = angular velocity x radius.

Christiano Ronaldo - 6 years, 3 months ago

Its SPEED which is asked, not VELOCITY.

Ninad Jadkar - 6 years, 3 months ago

In my opinion, speed is an ambiguous term here which can either mean angular speed or linear speed and thus the problem needs to be rephrased.

Prasun Biswas - 6 years, 3 months ago

@Prasun Biswas – Agreed. Circular motion can be measured as angular speed or linear speed. This question must be rephrased.

Michael Horton - 6 years, 3 months ago

@Prasun Biswas – In my opinion too.

Ram Hegde - 6 years, 3 months ago

@Prasun Biswas – i've edited the question

Vaibhav Prasad - 6 years, 3 months ago

I too have the same question and the thinking in my mind,as inthe abovecomment

Ram Hegde - 6 years, 3 months ago

i've edited the question

Vaibhav Prasad - 6 years, 3 months ago

Great, but that doesn't help me much since my previous answer is still marked incorrect.

Prasun Biswas - 6 years, 3 months ago

Just the TIP of the minute hand goes faster in B. Both minute hands (that is both a line all the way from center) goes 360 degrees in 60 minutes. If you had put them on top of each other you would see they move the same, but the tip of B's minute hand is further out and will have to travel further than the rest of both hands. I wondered if this was a trick question and wondered a long time to choose answer 2 or 4... Just rephrase it. ;)

Solveig Lyby - 6 years, 3 months ago

i've edited the question

Vaibhav Prasad - 6 years, 3 months ago

Basically, $v=\omega r$ , right?

Parag Zode - 6 years, 1 month ago

Christian Leonardi
Feb 18, 2015

Easy,u can do it with 10 seconds. First,the clocks around the world have same angular speed,Then Omega(Angular speed)xR(Radii)=V(speed)

Greater the Radii,greater the speed :)

Gamal Sultan
Feb 24, 2015

Speed of the tip of the minute hand in clock A within 60 minutes = 2(pi)r/60

Speed of the tip of the minute hand in clock B within 60 minutes = 2(pi)R/60

Since R> r, then

Speed of the tip of the minute hand in clock B is greater

Sunil Pradhan
Feb 19, 2015

The distance traveled in clock A = 2 × 22/7 × r = d

The distance traveled in clock B = 2 × 22/7 × R = D which is more than distance in clock A

Both the distances are traveled in same time of 60 min

so speeds are d/60 < D/60 so B travels fast.

Shaun Howarth
Feb 28, 2015

v=2 x pi x R/T, so if R bigger, v must be bigger

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