The small car that has a mass of 20 [kg] rolls freely on the horizontal track and carries the 5 [kg] sphere mounted on the light rotating rod with r = 0.4 [m]. A geared motor drive maintains a constant angular speed ω = 4 [rad/s] of the rod. If the car has a speed |v| = 0.6 [m/s] when θ = 0, calculate |v| when θ = 60◦ . Neglect the mass of the wheels and any friction.

Molten iron fills a mould, which has a volume of 200 cm cubed. calculate the volume when the iron cools and solidifies. molten iron has a density of 7.0g/cm cubed. in its solid state, iron has a density of 8.0g/cm cubed.

You have two photos of a person walking. one shows the person at the corner of third and main streets, the other shows the person at the corner of tenth and main streets. there are lampposts at every corner in this town, and the first picture shows it to be 10: 32: 00 exactly. the second picture shows it to be 10: 49: 30. you know three facts: (1) all of the clocks are synchronized; (2) there are exactly 12 equal-sized blocks per kilometer in this town; and (3) the streets that cross main in this area are numbered consecutively, with no interruptions. what is the person’s average speed in kilometers per hour?

Thermal radiation gets its name because