You can use some math to work this out and it's all fairly basic math.
Stars move at "sidereal" (yes, I know it looks like "side-real" but it's actually pronounced "sid-EAR-ee-al") speed. It's technically not the stars that move, but the ground beneath our feet. A "day" is 24 hours because that's how long it takes for the sun to go from directly above the meridian one day (true local noon) to the same position in the sky the following day. Except there are 365 days in a year and 360º in a circle. That means each day the Earth moves just fractionally less than 1º in our orbit around the sun. So technically the Earth does a full rotation every 23 hours, 56 minutes, and 4 seconds. It takes us 3 minutes and 54 seconds to catch up to the point where the Sun will appear to have moved (really due to our movement around the sun.)
To make the math easier... it takes the Earth about 1444 minutes to do a complete rotations. Divide 360º by 1444 and you get a value that says we move just about 1/4º (14.95 arc-minutes) per minute of real time. That's how far a star will appear to travel in one minute if the star is roughly above Earth's equator (declination 0º). Stars nearer to the Earth's poles will not appear to move so much. Expressed as "degrees" it works out to .249 degrees.
Hop over to a website such as
http://www.tawbaware.com/maxlyons/calc.htm and scroll down to find their "Angular Field of View Calculator", then punch in the focal length of your lens AND the crop-factor of your camera.
For example, if you were your 175mm lens and you have a Canon 400D (that's what your profile says) then your crop-factor is 1.6.
When I feed in these two values, it tells me the angular area of your sensor is:
Horizontal: 7.4º
Vertical: 4.9º
We've already established that the sidereal speed is about 1/4º per minute. That means that in just a 60 second exposure, a star will have moved 1/30th of the distance across your horizontal field of view. If you rotate the camera it will have moved about 1/20th of the distance across your vertical field of view. To get this, I'm dividing 7.4 by .249 for the horizontal dimension and I'm dividing the 4.9 by .249 to get the vertical dimension.
Your sensor is 3888 x 2592 pixels. That means that in the time it takes for the star to drift 1/30th of the distance across the
You would _definitely_ see star trails in that amount of time.
Suppose we switched to a wide angle lens such as Canon's 10-22mm and we zoom wide to a 10mm focal length with it. This changes things:
Horizontal: 96.7º
Vertical: 73.7º
NOW when we take the 60 second photo, a star near the equator would only have traveled 1/388th of the distance across the horizontal field of view. Based on the horizontal sensor resolution of 3888 pixels, 3888 ÷ 388 = about 10 pixels. That means in an enlarged size version of the image with close inspection you may notice the stars are elongated, but it'd be much harder to notice.
The wider the lens, the longer the exposure can be before you notice elongated stars.