Coin Rotation on Disc Calculation
This section details the calculation for determining how many times a coin rotates about its own center while rolling without slipping on the edge of a larger stationary disc.
Problem Parameters
- Radius of the stationary disc: $R = 10$ cm
- Radius of the rolling coin: $r = 1$ cm
Physics Principle
For a smaller circular object rolling without slipping around the outside of a larger fixed circular object, the total number of rotations ($N$) the smaller object makes about its center is given by the ratio of the sum of the radii to the radius of the rolling object. This accounts for both the rotation due to rolling along the path and the rotation due to the path itself being circular.
The formula is:
$N = \frac{R+r}{r}$Applying the Formula
Substitute the given radii into the formula:
$N = \frac{10 \text{ cm} + 1 \text{ cm}}{1 \text{ cm}}$ $N = \frac{11 \text{ cm}}{1 \text{ cm}}$ $N = 11$Result
The coin rotates 11 times about its center.
Important Questions from Circles, Chords and Tangents
There are two concentric circles. The radii of the two circles are 100 m and 110 m respectively. A wheel of radius 30 cm rolls on the smaller circle and another wheel rolls on the larger circle. After they have completed one revolution, it is found that the two wheels rolled equal number of times
on their respective axes. What is the radius of the other wheel ?- The length of a tangent drawn to a circle of radius 4 cm from a point 5 cm away from the center of the circle is:
- If SA and SB are tangents to a circle from an outside point S, such that SA = 12 cm and angle ASB = 60°. What will the length of chord AB be?
- In a circle, two chords of lengths x and y subtend the angles of $60^{\circ}$ and $90^{\circ}$ at the center respectively. Which of the following is correct in this scenario?
- A chord of length 24 cm is at a distance of 5 cm from the centre of a circle. The radius of the circle is ______ cm.
