## Mathematics 3Q: Mechanics MATHS3020

• School: School of Mathematics and Statistics
• Credits: 10
• Level: Level 3 (SCQF level 9)
• Typically Offered: Semester 2
• Available to Visiting Students: Yes

### Short Description

The aim of this course is to study the motion of a single particle, including central forces, conservation of energy and motion relative to a rotating frame of reference.

### Timetable

12 x 1hr lectures and 10 x 1hr tutorials in a semester.

### Requirements of Entry

Maths 2A, 2B and 2D at grade D3 or above.

Combined GPA of 9.0 or above on the three courses Maths 2C, Maths 2E and Maths 2F.

Full details of the requirements for a designated degree can be found in the University Calendar.

### Excluded Courses

Mechanics of Rigid and Deformable Bodies (??)

### Assessment

90% Examination, 10% Coursework.

Main Assessment In: April/May

Are reassessment opportunities available for all summative assessments? No

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below.

### Course Aims

The aim of this course is to extend the work on the basic two-dimensional motion of particles covered in Mathematics 2C.  Topics covered are:

1. Conservative forces.

2. Motion under the action of a central force.

3. Motion relative to a rotating frame of referenece.

### Intended Learning Outcomes of Course

By the end of this course students will be able to:

1. Formulate and solve the equations of motion for a point particle in a central force field.

2. Determine under what conditions circular orbits in central force-fields exist and determine their stability when they exist.

3. Determine whether a given force field is conservative or not and calculate a potential in the case of conversative force fields.

4. Deduce results about the motion of point particles on smooth axisymmetric surfaces.

5. State and apply the rotating axes theorem to deduce expressions for velocity and acceleration in an accelerating reference frame.

6.Formulate and solve the equations of motion for point particles in rotating frames of reference, for example projectile motion near the surface of the Earth.

None.