In “Set 1: Linear Motion & Tangential Relationships” using v = rω, a point on the edge of a record player is 0.15 m from the center and rotates at 33 rad/s. What is the linear speed of that point?
Use s = rθ, v = rω, and aₜ = rα to solve these.
Use the tangential speed relation $v=r\omega$. With $r=0.15\,\text{m}$ and $\omega=33\,\text{rad/s}$, $$v=(0.15)(33)=4.95\,\text{m/s}.$$ So the point’s linear speed is $4.95\,\text{m/s}$ (about $5.0\,\text{m/s}$).
What you are converting here
The record player’s angular speed $\omega$ (how fast it turns in rad/s) can be turned into a linear or tangential speed $v$ (how fast a point on the rim moves in m/s) if you know the radius $r$.
Apply the tangential speed formula
For circular motion, $$v=r\omega.$$ Substitute the given values: $$v=(0.15\,\text{m})(33\,\text{rad/s})=4.95\,\text{m/s}.$$
Quick units check
Radians are dimensionless, so $(\text{m})(\text{rad/s})$ simplifies to $\text{m/s}$, which matches the units of linear speed.
Final result
$$v=4.95\,\text{m/s}.$$
- Forca centripetale (m=3 kg, r=1 m, T=2 s)
- Is Uniform Circular Motion Accelerated? Justified
- Electric Field on the Axis of a Charged Ring
- Hammer vs Feather in Vacuum: Which Value Differs?
- Angle of Refraction as the Dependent Variable
- 52T and 9T bike gear ratio: wheel turns per crank
- Parallel circuit diagram: 1 battery, 3 lights, switch
- Change in Temperature of Heated Copper Pipe
Comments (0)
Please to leave a comment.