Using velocity and acceleration, describe the uniform circular motion of an object.
State an expression, in terms of $R$ and $\omega$, for the ball’s speed $v$.
Determine an expression, in terms of $v$ and $\omega$, for the ball’s centripetal acceleration.
The ball in (b) is shown in Fig. 1.1, with line OB making an angle $\theta$ to line OP. Determine an expression, in terms of $R$ and $\theta$, for the shadow’s displacement $x$ from P.
At time $t = 0$, the value of $\theta$ is zero. State an expression for $\theta$ in terms of $\omega$ and $t$.
Use the results from (c)(i) and (c)(ii) to show that $x$ is given by $x = R \sin \omega t$.
Explain, using the equation in (c)(iii), why the shadow of the ball on the screen can be modelled as simple harmonic motion.
The circular motion of the ball in Fig. 1.1 has a diameter of $0.46\,\text{m}$ and an angular speed of $1.9\,\text{rad s}^{-1}$. For the simple harmonic motion of the shadow of the ball in Fig. 1.1, calculate the amplitude.
The circular motion of the ball in Fig. 1.1 has a diameter of $0.46\,\text{m}$ and an angular speed of $1.9\,\text{rad s}^{-1}$. For the simple harmonic motion of the shadow of the ball in Fig. 1.1, calculate the period.
The circular motion of the ball in Fig. 1.1 has a diameter of $0.46\,\text{m}$ and an angular speed of $1.9\,\text{rad s}^{-1}$. For the simple harmonic motion of the shadow of the ball in Fig. 1.1, calculate the maximum acceleration.
On Fig. 1.1, draw, and label with the letter A, the position of the shadow on the screen when the shadow has its maximum positive acceleration.