Basic ideas (for sheet) Work = F.d W = DK Power = dW/dt (=F.v) Kinetic Energy: K = ½ mv2 P.E. Ug = mgh Uel = ½ k(x-xo)2 F = -dU/dx (e.g. Spring: F = -k(x-xo) Mech. Eng. conserved if only conservative forces do work. Dissipative forces convert some Mech. Eng. to thermal energy. Center of Mass R = S(miri)/Smi P= mv F = dP/dt => momentum is conserved if there are no outside forces Rocket formula: (dM/dt)V=Ma v-vo =-Vln(Mo/M) Defns: Elastic, Perfectly inelastic, etc. for collisions, Conservative forces

A car accelerates at a constant rate of 2 A car accelerates at a constant rate of 2.60 m/s2 along a straight line. Assuming that its tires roll without slipping on the road, and that they have a diameter of 45.0 cm, what is the angular acceleration of each tire? If the car started from rest, what would be the angular velocity of the tires after 4.0 seconds of acceleration? (8 knew how to answer this [but only 4 got it right]; 13 made various errors [mainly not distinguishing v and w] 23 no answer). .585m/s^2. I multiplied the acceleration by the radius of the tires. The angular velocity would be 10.4m/s. I got this by multiplying the acceleration by the time provided. Using the equation a = v^2/r, we get that the angular acceleration to be 30.04 m/s^2. The angular velocity of the tires would be 120.2 m/s.

The angular acceleration of each tire is 11. 57 radians/s^2 The angular acceleration of each tire is 11.57 radians/s^2. The angular velocity of the tires would be 2.89 rads/s. linear acceleration 2.6 m/s^2 radius of curvature 0.225 m angular acceleration 11.6 m/s^2 angular velocity after 4s 11.6*4= 46.4m/s (almost right, but units are rad/s^2 and rad/s)

Chapter 10 problems

Angular displacements are NOT 3-D vectors!! They don’t add commutatively!

AVERAGE: 53.6/78 = 68.7%

The direction of the resulting torque would be up. Up/Down: 9 Into/out page: 6 CW/CCW: 5 Other: 4 No answer: 19 Front view Side view P S The direction of the resulting torque would be up. The torque would move the wheel like a pendulum swinging downward clockwise then counterclockwise back and forth. the direction of the resulting torque is toward or out of the screen. It might also be to the right. The torque would be pointing straight ahead; i.e., if the pole is parallel to the z axis and the wheel is parallel to the x axis, the torque is parallel to the y axis.

Rotational Inertia for Selected objects and rotation axes: HR&W Table 10-2

Chapter 10 problems