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