Circular Motion

Question 1

How to find angle of sector in radians

Answer 1

Arc length / Radius

Question 2

Define angular velocity

Answer 2

Rate of change in angle of an object moving in a circular path

Question 3

Define Centripetal force

Answer 3

A force that keeps a body moving at a uniform speed along a circular path. Always perpendicular to velocity of body.

Question 4

How to turn degrees into radians

Answer 4

Divide degrees by 180/Pi

Question 5

Derive a = v^2/r

Answer 5

Considering an object moving at constant speed v along a a circular path from point A to B subtending a small angle, the angle will be equal to the arc length / radius. Since the angle is small, arc length is almost a straight line, therefore arc length can be written as the velocity of the object multiplied by the time elapsed from point A to point B, due to the fact that displacement is equal to velocity * time. Velocity at point A and B are different due to the change in direction. Magnitude remains constant. By creating a vector triangle with Va and Vb, the angle between them will be equal to the angle subtended by the object. By resolving vectors, we find the resultant vector of the 2 velocities to be equal to their change in velocity. Using angle = arc length / radius, and remembering that arc length is almost a straight line, angle subtended is also equal to change in velocity / velocity. Equating both equations we get v^2/r is equal to Change in velocity/time, which is the definition of acceleration. In turn, this means a = v^2/r

Question 6

How to investigate circular motion with bung

Answer 6

Connect a bung to a string. Put string through cylinder, then connect a weight to other end of string. Choose desired radius from bung to cylinder, then attach paper clip to the string under the cylinder, above weight to prevent weight moving and changing radius. Swing the bung in a horizontal circle, increase velocity of swing until paper clip is at the top of cylinder and stops moving. This indicates that the centripetal force is equal to the weight. Find Time period of bung by time taken for 10 revolutions using a stopwatch, then dividing time by 10 for accuracy. 2pi divided by time period gives angular velocity, angular velocity multiplied by radius gives velocity of bung. Repeat experiment with varying weights, plot F against v^2, gradient gives m/r which should be straight line through origin.

Question 7

Equation for velocity of conical pendulum

Answer 7

tan(θ) = Velocity ^2 / Radius * Gravity