A giant toy car with big wheels has a total mass (including the wheels) of 0.21 kg. The car has 4 wheels and each wheel has radius of 3.3 m and a moment of inertia of 0.22 kg m2. The car is attached to a horizontal spring. The spring is inititally unstretched and the car is given an initial speed of 1.9 m/s away from the spring. The car moves forward 0.38 m before it stops and is pulled back by the spring. The wheels roll without slipping the entire time. What is the spring constant?

A simple pendulum is formed of a rope of length L 1.6 m and a bob of mass m. When the pendulum makes an angle 0 = 10° with the vertical, the speed of %3D the bob is 2 m/s. The angular speed, e', at the lowest position is equal to: (g %3D 10 m/s^2) 1.32 rad/s 0.98 rad/s 0.63 rad/s 2.93 rad/s

I have been stuck on this question for a while. I broke it down into parts and solved for velocity but I think I am doing something wrong.

As shown in right Figure, a pulley has a moment of inertia j=0.5kg m^2 and a radius r=30 cm. The spring has a spring constant k=20 N/m and the block has a mass m=2.0 kg. Assume the block-pulley system starts from rest and no initial stretch is applied on the spring.  (a) How far will the block move along the inclined? (b) If the block slides 1.00 m along the inclined, what is its speed?

A cylindrical metal drum, with a radius of 0.25 m, has an inertia of 11.0.kg. The drum is hollow and you may neglect the inertia of the top and bottom of the drum. The drum is free to rotate about an axle that runs through its centre and along its long axis. A cord is wrapped around the drum. The cord is pulled straight from the drum with a constant force of 60 N. As the cord unwinds, the drum rotates, with no slippage between the cord and the drum. (a) Calculate the work done by person pulling the cord as the drum rotates through 100 radians. Give your answer in Joules (b) Assuming the drum starts from rest, what is the rotational speed of the tyre after it has rotated through 100 radians? Give your answer in rad.s

The smooth hollow tube assembly rotates about a vertical axis with angular velocity ω=θ˙=3.8ω⁢=θ˙=3.8 rad/s and ω˙=θ¨=−2.4ω˙=θ¨=-2.4 rad/s2. A small 0.23-kg slider P moves inside the horizontal tube portion under the control of the string which passes out the bottom of the assembly. If r=0.88r=0.88 m, r˙=−1.9r˙=-1.9 m/s, and r¨=3.8r¨=3.8 m/s2, determine the tension T in the string and the horizontal force Fθ exerted on the slider by the tube. T is positive in tension, and Fθ is positive if in the positive θ direction.