How many degrees and radians do the minute hand and hour hand of a clock move in 15 minutes?

Question

This is from Chapter 4, Exercise 4-3, #36 of Fundamentals of Technical Mathematics (2nd edition): If it takes you 15 minutes to do this problem, how many degrees and radians do the (a) minute hand and (b) hour hand of a clock move in that time?

Answer 1

The minute hand moves 15/60, or 1/4, of a circle, which is 90 degrees, which is pi/2 radians. The hour hand moves 1/4 of an hour, which, since an hour is 360 degrees / 12 hours = 30 degrees per hour, is 1/4 * 30 = 7.50 degrees, which is pi/24 radians.

Answer 2

The second hand will move 90 degrees which is about 1.57 radians.
The hour hand is going to move 1/4 of an hour.
Since there are 12 hours on the clock face the hand will be moving 1/4 of 1/12 of the way around the clock.

This equals:
(1/4)*(1/12)=1/48

So the hour hand moved 1/48 of the way around. To convert this to degrees simply take 1/48 of 360 degrees.

(1/48)*(360)=7.5

This gives you 7.5 degrees. Converted to radians you get about 0.131

Answer 3

They move 1/4 of the clock, so 90 degrees.

Answer 4

The hands move 90 degrees.

Answer 5

Many physics subjects take care of the relationships between some "linear" quantities (like force) and "angular" quantities (like angular velocity). Such relationships place self assurance in the actuality which you would be waiting to stipulate an physique of strategies in words of two lengths--specially, you would be waiting to divide an arc era by using ability of a radius, and upward push up with an physique of strategies. Angles measured that approach come out in radians (properly it is the definition of a radian). considering that radians can be expressed as a sensible ratio of two lengths, that variety of makes them the "ordinary" unit to make the main of in subjects that relate linear and angular quantities. To take an illustration--say an ant is on the rim of a rotating disk of radius 10 cm. if he's moving at 3 cm/sec, what's his angular velocity? properly, could you in straightforward terms divide the three by using ability of the 10, think ofyou've have been given won your respond, and it robotically comes out in rad/sec pondering of ways radians are defined. in case you needed the respond in some unique angular unit (like tiers), you're able to could divide 3 by using ability of 10 and then use some conversion element (a hundred 80/?). So in one journey, the reason you make the main of radians is that it simplifies the math (eliminates conversion components) in subjects that relate linear and angular quantities.