Circular motion Problem set A Answers

\(\mathbf{r} = \begin{pmatrix} 3\cos 4t \\ 3\sin 4t \end{pmatrix}\)

\(\mathbf{r} = \begin{pmatrix} 2\sin 3t \\ 2\cos 3t \end{pmatrix}\)

1. (a) |r| = 5 for all t, a circle of radius 5 m
2. (b) |r| = 1.5 for all t, a circle of radius 1.5 m

1. (a) Centre \((8, −2)\), radius 1.5 m
2. (b) Centre \((−3, 5)\), radius 2 m

1. (a) Anticlockwise, 2.09 s
2. (b) Clockwise, 12.6 s
3. (c) Clockwise, 1.57 s

1. (a) \(\mathbf{r} = \begin{pmatrix} 2\cos 5t \\ 2\sin 5t \end{pmatrix}\)
2. (b) 2 m from the centre: a circle of radius 2 m
3. (c) 1.26 s

1. (a) \(\mathbf{r} = \begin{pmatrix} 5\sin 3t \\ 5\cos 3t \end{pmatrix}\)
2. (b) |r| = 5 for all t, a circle of radius 5 m
3. (c) (0.706, −4.95)

1. (a) \(\mathbf{r} = \begin{pmatrix} 15\cos \dfrac{\pi t}{15} \\ 17 + 15\sin \dfrac{\pi t}{15} \end{pmatrix}\) m
2. (b) 30.0 m
3. (c) 3.14 m s⁻¹

1. (a) \(\mathbf{r} = \begin{pmatrix} 6\cos \dfrac{t}{2} \\ 6\sin \dfrac{t}{2} \end{pmatrix}\)
2. (b) |r| = 6 for all t, a circle of radius 6 m
3. (c) |v| = 3 m s⁻¹, constant